FROM  -THE -LIBRARY-  OF 
•WILLIAM -A  HILLEBRAND 


ENGINEERING  LIBRARY 


STANDARD  TABLE 

OF 

ELECTROCHEMICAL  EQUIVALENTS 

AND 

THEIR  DERIVATIVES 


Standard  Table 


OF 


ELECTROCHEMICAL  EQUIVALENTS 

AND 

Their  Derivatives 

WITH 

Explanatory  Text  on  Electrochemical  Calculations 

Solutions  of  Typical  Practical  Examples  and 

Introductory  Notes  on  Electrochemistry 


BY 


CARL    HERING,    M.E.,    D.Sc. 

Past  President  American  Electrochemical  Society  and  American 
Institute  of  Electrical  Engineers.    Author  of 
"Conversion  Tables" 

AND 

FREDERICK    H.   GETMAN,  Ph.D. 

Research  Chemist 
Formerly  Associate  Professor  of  Chemistry  in  Bryn  Mater  College 


NEW  YORK 

D.  VAN  NOSTRAND   COMPANY 

25  PARK  PLACE 

1917 


\>v 


.COPYRIGHT,  IQI?,  BY 

NOSTRAND     COMPANY 


LIBRARY 


THE-PLIMPTON-PRESS 
NORWOOD-MAS  S-U-S'A 


PREFACE 

The  chief  purpose  of  this  publication  is  to  serve  as 
a  reference  book  on  account  of  the  tables  and  other 
data  given  in  it,  and  not  as  a  treatise  on  electro- 
chemistry in  general;  sufficient  explanatory  text  has 
however  been  added  to  enable  the  data  to  be  used 
for  most  purposes  without  the  need  of  a  further 
treatise  on  the  subject.  To  make  the  data  available 
also  to  the  student,  electroplater,  engineer,  and 
others  who  may  not  have  made  a  special  study  of 
chemistry  and  electrochemistry,  the  descriptive  text 
has  been  given  in  elementary  and  easily  understood 
terms. 

In  Electrochemical  Industries  (later  Metallurgical  & 
Chemical  Engineering)  for  January,  1903,  one  of  the 
present  authors,  Carl  Hering,  published  a  very 
complete  table  of  electrochemical  equivalents  calcu- 
lated from  the  then  best  fundamental  values.  Since 
then  a  more  accurate  value  of  the  fundamental 
electrochemical  constant,  based  on  silver,  has  been 
adopted  internationally  and  quite  a  number  of  the 
atomic  weights  have  been  changed.  The  table  in 
the  present  book  has  therefore  been  entirely  recalcu- 
lated by  its  author  from  the  latest  and  best  inter- 
nationally adopted  fundamental  values,  including  the 
atomic  weights  for  1917.  It  has  also  been  enlarged 
to  include  all  the  elements  and  practically  all  of 
their  valences.  The  equivalents  are  given  in  terms 
of  various  units,  including  in  each  case  their  re- 
ciprocals. 

995706 


vi  PREFACE 

The  methods  of  making  electrochemical  calcula- 
tions involving  these  equivalents  are  described  by 
means  of  a  number  of  typical  practical  examples 
accompanied  by  explanatory  notes.  A  brief  descrip- 
tion of  some  of  the  elementary  principles  of  chem- 
istry involved  in  such  calculations,  has  been  added. 

Some  of  the  conceptions  and  simplified  methods 
of  calculation  described  in  the  text  may  differ  from 
those  more  generally  taught  or  found  in  textbooks; 
they  are  offered  here  merely  as  suggestions  which 
lead  to  the  same  result  as  the  older  and  more  com- 
plicated ones;  the  latter  are  also  described  as  al- 
ternatives to  be  used  by  those  who  prefer  them. 

The  rapid  developments  of  recent  years  in  the 
physical  conceptions  of  electrochemical  phenomena 
made  it  desirable  to  include  an  introductory  descrip- 
tion of  them  in  a  section  on  the  Electronic  Theory. 
This,  and  a  section  on  Electrolysis  which  includes  a 
brief  explanation  of  the  dissociation  theory,  have 
been  prepared  by  the  other  author,  Frederick  H. 
Getman. 

The  authors  acknowledge  their  indebtedness  to 
Dr.  J.  W.  Richards  for  revising  and  bringing  up  to 
date  his  table  of  the  valences  which  the  elements 
have  in  their  more  usual  combinations.  Also  to  the 
Bureau  of  Standards  for  most  of  the  fundamental 
constants  and  for  valuable  advice  and  assistance. 

CARL  HERING 
FREDERICK  H.   GETMAN 

Philadelphia,  Pa.,  and  Stamford,  Conn., 
June,  1917. 


CONTENTS 

Preface v 

Introduction ix 

PART  I 

Section     I.    Fundamental  Laws 1 

Section    IE.     Fundamental  Data  and  Description  of  the 

Tables 7 

Section  HI.     Table     I.     Electrochemical   Equivalents   by 

Weight 12 

Table    n.     Grams  per  Ampere-hour  in  the 

Order  of  Magnitude 21 

Table  III.    Electrophysical    Equivalents    by 

Volume 23 

Table  IV.    Valences    of    the    Elements    in 

Their  Combinations 24 

Section  IV.     Calculations     Involving     Electrochemical 

Equivalents.    Examples 28 

PART  H 

Section    V.    Electrolysis.    Theory  of  Electrolytic  Dissoci- 
ation.    Faraday's   Law.     Coulometers ...       63 
Section  VI.     The  Electronic  Theory 73 


Appendix     I.    Valence 91 

Appendix    n.    Elementary  Principles  of  Chemical  Reac- 
tions and  Calculations .*....  112 

Appendix  m.     Conversion  Factors  Used  in  Electrochemical 

Calculations 120 

Appendix  IV.     Glossary  of  Terms 123 

Index 125 


Vll 


INTRODUCTION 

The  chief  purpose  of  the  present  book  is  to  pro- 
vide a  table  of  constants,  based  on  the  latest  and 
best  fundamental  values,  for  making  calculations  of 
the  amounts  of  substances  electrolytically  deposited, 
dissolved,  or  otherwise  chemically  changed,  by  an 
electric  current,  and  to  explain  by  means  of  a  series 
of  typical  practical  examples  and  descriptive  text, 
how  such  calculations  are  made.  This  forms  Part  I. 

In  many  of  the  simplest  kinds  of  calculations  in- 
volving merely  the  quantities  of  metal  deposited  or 
dissolved,  or  the  quantities  of  gases  evolved  by  a 
given  current,  or  the  reverse,  the  calculations  by 
means  of  the  constants  in  the  table  are  so  extremely 
simple,  consisting  merely  of  a  multiplication,  that  no 
further  knowledge  of  chemistry  or  the  laws  of  elec- 
trolysis is  required,  all  the  involved  parts  of  the 
complete  calculations  having  been  made  in  the 
preparation  of  the  table. 

Many  of  these  calculations  being  greatly  simplified 
by  considering  the  chemical  valence  as  a  separate 
factor,  as  distinguished  from  using  chemical  equiva- 
lents, a  description  of  the  significance  which  the 
valences  have  in  electrochemistry  is  given  in  Ap- 
pendix I;  the  application  of  valences  to  such  calcu- 
lations is  described  in  the  examples.  The  older 
methods  are  also  described  for  the  benefit  of  those 
who  do  not  understand  or  do  not  agree  with  the 
suggested  conception  of  the  meaning  and  application 
of  valence  to  electrochemical  calculations  which  is 


X  INTRODUCTION 

believed  to  be  in  agreement  with  the  modern  and 
generally  accepted  electronic  theory. 

The  physical  conception  of  electrochemical  phe- 
nomena has  been  greatly  developed  in  recent  years, 
and  altho  this  does  not  change  the  simplest  ways  of 
making  the  calculations  by  the  use  of  this  table,  yet 
it  is  of  interest  and  of  use.  This  has  been  briefly 
summarized  in  Part  II,  which  includes  also  a  brief 
treatise  on  electrolysis  as  based  on  the  modern 
dissociation  theory. 

The  elementary  principles  of  chemistry  involved 
in  the  usual  calculations  are  briefly  summarized  in 
Appendix  II;  for  the  more  involved  cases  a  fur- 
ther knowledge  of  chemistry  and  electrochemistry  is 
necessary. 

A  list  of  the  principal  conversion  factors l  used  in 
such  calculations  is  given  in  Appendix  III. 

In  place  of  a  glossary  of  the  terms  used  in  this 
book,  the  places  in  the  text  where  they  have  been 
defined  and  used  are  given  in  Appendix  IV. 

1  Taken  from  Bering's  Conversion  Tables. 


PART    I 

-  *  °    j  •*  j  *  * 
Section  I 

FUNDAMENTAL   LAWS 

The  simplest  and  most  basic  law  of  electrolysis 
refers  to  the  elements  when  they  are  in  their  gaseous 
state,  or  in  the  state  of  vapor.  When  in  this  state 
it  is  true  alike  for  every  element  that  to  set  free  a 
liter  of  this  gas  or  vapor  requires.. the  same  constant 
amount  of  electricity  in  coulombs  or  ampere-hours 
when  there  is  one  atom  to  the  molecule  and  when 
the  change  of  valence  is  unity.  For  those  elements 
in  which  there  are  two  or  more  atoms  to  the  molecule 
it  will  require  two  or  more  times  this  constant  quan- 
tity of  electricity,  in  direct  proportion;  and  for  any 
other  change  of  valence  the  constant  must  also  be 
increased  in  direct  proportion.  This  law  applies 
strictly  to  perfect  or  ideal  gases  only,  and  it  may  be 
true  that  some  of  the  gaseous  elements  deviate 
slightly  from  this  perfect  state;  the  latter  may  be 
due  to  a  lack  of  precision  in  our  knowledge  of  the 
physical  constants  of  the  elements  in  their  gaseous 
form.  But  the  deviations  do  not  seem  to  be  greater 
than  fractions  of  one  percent  and  they  may  therefore 
be  neglected  in  most  cases. 

From  the  latest  and  best  fundamental  physical 
constants,  which  are  given  in  Section  n,  this  funda- 
mental constant  for  perfect  gases  is  4,309.7  coulombs, 

1 


2  ELECTROCHEMICAL  EQUIVALENTS 

or  1.1971  ampere-hours,  per  liter  of  gas  or  vapor, 
at  0°C.  and  760  mm.  atmospheric  pressure ;  or  exactly 
1  ampere-hour  per  liter  at  a  temperature  of  53.82°  C. 
The  fifth  place  of  figures  is  uncertain.  This  constant 
applies  directly  to  a  monatomic  element  (meaning 
oris/ fcayiiig ;  only  one  atom  to  the  molecule)  like 
sodium  vapor  „  for  instance,  when  the  change  of 
valence  is  unity;  for  a  diatomic  element  (two  atoms 
to  the  molecule)  like  hydrogen,  and  when  the  change 
of  valence  is  unity,  this  constant  must  be  multiplied 
by  2;  for  a  diatomic  element  like  oxygen,  and  when 
the  change  of  valence  is  2  (the  element  is  then  called 
bivalent  or  di-valent)  the  constant  must  be  multiplied 
by  2  x2;  etc. 

As  this  constant  is  the  same  for  all  the  elements 
and  is  independent  of  then*  atomic  weights  or  vapor 
densities,  this  relation  between  the  amount  of  gas 
or  vapor  and  the  amount  of  electricity  required  to 
set  it  free  is  the  simplest  and  most  direct  one,  and 
may  therefore  be  said  to  be  the  most  fundamental 
one.  It  may  be  said  to  be  the  physical  relation  as 
distinguished  from  the  chemical  relation  more  com- 
monly used.  It  may  be  deduced  by  combining  the 
generally  accepted  law  of  Faraday  with  that  of  Avo- 
gadro,  which  latter  states  that  one  gram  molecule 
of  every  element  occupies  the  same  volume  when  it 
is  in  its  state  of  gas  or  vapor,  when  the  temperatures 
and  pressures  are  the  same. 

When  the  amounts  of  electrolytic  gases  of  any  of 
the  elements  are  desired  in  terms  of  their  volume,  as 
distinguished  from  then*  weight,  this  relation  is  also 
the  simplest  and  most  direct  one  to  use  for  making 
the  calculations;  and  as  it  happens  that  all  the  six 
gaseous  elements  which  might  be  evolved  electrolyti- 
cally  are  diatomic  at  ordinary  temperatures,  doubling 


FUNDAMENTAL  LAWS  3 

this  constant  will  make  it  apply  to  all  of  them  for 
each  unit  change  of  valence.  Derivatives  of  this 
constant,  for  convenience  in  calculations  concerning 
these  six  elements,  are  given  in  Table  HI. 

But  hi  most  cases  the  elements  concerned  in 
electrolytic  calculations  are  not  in  their  gaseous 
state  and  sometimes  they  merely  undergo  a  chemical 
change  and  are  not  set  free  or  dissolved.  This 
simple  physical  relation  is  then  not  the  most  con- 
venient one  to  use.  Moreover  to  specify  a  quantity 
of  a  substance  in  terms  of  its  weight  (or  mass) 
instead  of  its  volume,  is  often  the  most  rational 
way,  and  may  simplify  other  subsequent  calculations; 
for  gases  furthermore  the  quantity  is  then  independ- 
ent of  the  otherwise  disturbing  effect  of  the  tempera- 
ture and  pressure. 

When  the  weights  of  the  quantities  are  concerned 
the  simplest  relation,  deduced  from  Faraday's  law, 
is  that  every  gram  ion  involved  in  an  electrolytic 
change,  no  matter  of  which  element,  requires  the 
same  number  of  coulombs  or  ampere-hours  of 
electricity,  per  unit  change  of  valence;  if  the  change 
of  valence  is  two,  three,  etc.,  the  amount  of  electricity 
is  two,  three,  etc.,  times  as  great. 

From  the  latest  and  best  fundamental  physical 
constants  given  in  Section  II,  this  constant  is  96,494 
coulombs  or  26.804  ampere-hours  per  gram  ion. 
This  is  called  a  "faraday,"  a  name  which  has  not 
yet  been  formally  adopted  but  is  sanctioned  by  good 
usage  and  has  been  generally  accepted.  For  many 
calculations  however  this  constant  is  a  very  incon- 
venient and  awkward  one  to  use;  the  following 
derivatives  of  it  will  often  be  found  more  convenient. 
Table  I  is  based  on  this  constant. 

The  quantity  of  electricity  required  to  electrolyze 


4  ELECTROCHEMICAL  EQUIVALENTS 

a  given  quantity  of  any  element  by  weight,  and  for 
each  unit  change  of  valence,  is  equal  to : 

96.494  -T-  atomic  weight,  in  coulombs  per  milligram ; 
26.804  -=- atomic  weight,  in  ampere-hours  per  gram; 
12,158.  -T-  atomic  weight,  in  ampere-hours  per  pound. 

The  reciprocals  of  these  standard  values  are : 

Atomic  weight  x  0.010363,  in  milligrams  per  coulomb; 
Atomic  weight  x  0.037308,  in  grams  per  ampere-hour; 
Atomic  weight  x  0.082250,  in  pounds  per  1000  ampere-hours. 

The  physical  meaning  of  these  constants  is  that 
they  would  be  the  actual  values  for  a  hypothetical 
element  having  an'  atomic  weight  of  exactly  unity. 
As  the  atomic  weight  of  hydrogen  is  1.008  they 
represent  that  element  to  within  a  little  less 
than  1%. 

These  constants  are  for  a  change  of  valence  of 
unity;  when  it  is  other  than  unity  those  of  the 
first  group  must  be  multiplied  by  the  change  of 
valence,  or  those  of  the  second  group  (the  recipro- 
cals) divided  by  it. 

The  term  "change  of  valence "  is  used  here  instead 
of  the  shorter  one  "valence"  used  in  most  books, 
because  the  latter  term  by  itself  may  sometimes  lead 
to  very  incorrect  results;  it  is  not  always  the  valence 
which  an  element  has  in  a  chemical  compound  which 
governs  the  electrolytic  quantities  involved,  but  it  is 
always  the  change  of  valence  during  electrolysis 
which  is  the  true  governing  factor,  that  is,  it  is 
always  the  difference  between  the  valences  before 
and  after  electrolysis.  Faraday's  law  stated  in  terms 
of  valence,  as  it  usually  is,  fails  to  apply  in  some 
cases,  but  when  stated  in  terms  of  the  change  of 
valence  it  becomes  a  universal  law. 


FUNDAMENTAL  LAWS  5 

The  valence  of  any  element  in  its  free,  uncombined 
state  must  be  considered  to  be  zero,  because  the 
term  valence,  in  Faraday's  law  at  least,  must  be 
interpreted  to  mean  the  number  of  bonds  per  atom 
which  hold  it  in  combination  with  another  element, 
hence  when  the  element  is  no  longer  combined  these 
bonds  of  course  no  longer  exist.  Therefore  when  an 
element  has  been  set  free  by  electrolysis  it  means 
that  it  has  changed  its  valence  from  what  it  had  in 
the  compound  to  zero;  in  that  specific  case  therefore, 
and  only  in  that  case,  is  the  "valence"  numerically 
equal  to  the  "change  of  valence,"  and  it  is  only  this 
particular  case  and  not  the  more  general  one,  that 
the  textbooks  can  refer  to  when  they  give  Faraday's 
law  in  terms  of  "valence"  instead  of  more  broadly 
and  more  correctly  in  terms  of  the  "change  of 
valence."  For  further  explanations  see  the  examples 
in  Section  IV  and  Appendix  I  on  Valence. 

It  follows  from  the  above  that  the  same  current 
will  electrolyze  chemically  equivalent  quantities  per 
minute.  For  some  cases  this  is  a  convenient  way  of 
stating  Faraday's  law;  the  valence  then  does  not 
enter  into  the  calculation  as  it  is  already  embodied 
in  the  chemically  equivalent  quantities.  This  is 
illustrated  in  the  examples,  Section  IV. 

Another  fundamental  law  of  electrolysfs  is  that  at 
the  cathode  there  will  always  appear  that  kind  of  a 
chemical  reaction  which  is  called  a  reduction,  which 
always  involves  a  reduction  of  the  valence,  while  at 
the  anode  there  will  always  appear  the  opposite  or  re- 
versed kind  called  oxidation,  or  better,  adduction, 
which  always  involves  an  increase  of  valence.  When 
chemical  reductions  and  adductions  or  oxidations  are 
thus  interpreted  in  terms  of  changes  of  valence,  for 
simplifying  conceptions  and  calculations,  it  becomes 


6  ELECTROCHEMICAL  EQUIVALENTS 

necessary  to  couple  with  the  valence  the  algebraic 
signs  +  or  -  which  it  must  have  in  order  to  cor- 
respond with  the  direction  of  the  current  which 
produces  the  reaction.  For  further  explanation  see 
Appendix  I  on  Valence. 


Section  n 

FUNDAMENTAL  DATA  AND  DESCRIPTION 
OF  THE  TABLES 

The  fundamental  constants  on  which  the  values 
in  this  table  are  based  are  the  electrochemical 
equivalent  of  silver,  0.001 118  00  gram  per  coulomb, 
which  has  been  accepted  internationally,  and  the 
atomic  weight  of  silver  107.88  which  is  the  inter- 
nationally accepted  value  for  1917.  Both  have  been 
accepted  by  the  Bureau  of  Standards. 

Theur  quotient  gives  the  resulting  value  96493.7 
coulombs  per  univalent  gram  ion  (log  =  4.984  4991) 
for  the  electrochemical  constant  called  the  faraday; 
for  most  purposes  this  is  more  conveniently  rounded 
off  to  96  500,  the  error  being  less  than  1/100  of  1  %. 
The  equivalent  of  the  former  is  26.803  8  ampere- 
hours  (log  =  1.428  1966),  conveniently  rounded  off 
to  26.8  (error  about  1.5  hundredths  of  1%).  On  the 
above  basis  the  faraday  necessarily  becomes  a  de- 
rived quantity  and  is  therefore  not  the  fundamental 
constant. 

The  atomic  weights  of  all  the  elements  are  the 
international  values  for  1917,  based  on  oxygen  =  16, 
but  as  the  electrochemical  equivalents  are  absolute 
and  not  relative,  they  would  of  course  be  the  same 
for  atomic  weights  based  on  hydrogen  =  1.  These 
atomic  weights  were  obtained  directly  from  Dr. 
F.  W.  Clarke,  Chairman  of  the  International  Com- 
mittee. The  table  includes  the  constants  for  all  the 
elements  excepting  only  the  six  noble  gases  which 
enter  into  no  combinations. 

7 


8  ELECTROCHEMICAL  EQUIVALENTS 

Altho  most  of  the  atomic  weights  are  not  known  to 
more  than  four  places  of  figures,  the  constants  in 
the  table  have  been  carried  out  uniformly  to  five 
places  in  order  that  when  more  accurate  atomic 
weights  become  known  the  constants  can  be  corrected 
by  proportion.  In  order  that  all  calculations  may  be 
made  by  a  multiplication,  the  reciprocals  of  all  the 
values  have  also  been  given,  thereby  eliminating  all 
calculations  by  division.  The  constants  are  given  in 
terms  of  the  three  most  commonly  used  compound 
units,  milligrams  per  coulomb,  grams  per  ampere- 
hour  and  pounds  per  1000  ampere-hours. 

The  different  valences  for  which  the  constants  are 
given  in  Table  I  are  believed  to  include  most  of  the 
cases  occurring  in  practice,  either  as  valences  or  as 
changes  of  valences.  In  some  cases  the  constants 
for  a  valence  1  have  been  included  even  tho  that 
valence  may  not  occur  in  practice,  in  order  to  facilitate 
calculating  the  constants  for  other  valences  or  changes 
of  valence  than  those  given,  by  a  mere  multiplication 
or  division  by  the  new  valences;  to  avoid  confusion 
these  values  are  italicized  hi  Table  I.  Near  the  end 
of  this  table  it  is  shown  how  to  calculate  the  constants 
for  any  other  valences;  thus  if  n  is  the  constant 
given  in  any  of  the  columns  for  a  valence  v,  then  for 
any  other  valence  x  multiply  the  constant  n  by  v/x 
or  by  x/v  as  stated  in  that  column.  For  the  valences 
which  the  elements  have  in  their  various  compounds 
see  Table  IV. 

The  last  line  of  values  gives  the  general  formulas 
and  constants  for  calculating  any  of  the  values  in  the 
table  for  any  atomic  weight  y  and  any  valence  *, 
based  on  the  internationally  accepted  fundamental 
electrochemical  equivalent  as  given  above. 

Table  II  gives  the  constants  of  column  7  of  Table  I, 


DESCRIPTION  OF  TABLES  9 

arranged  in  the  order  of  the  magnitude  of  the  electro- 
chemical equivalents  of  the  elements.  For  other 
valences  than  those  given  in  the  table  there  would  of 
course  be  additional  values  hi  this  supplementary 
table.  The  values  given  in  italics  in  Table  I  have 
been  omitted  in  Table  II. 

The  constants  in  Table  I  are  hi  terms  of  the  weights, 
but  when  the  volumes  are  desired  of  those  elements 
which  are  gases,  the  calculations  of  the  amounts  set 
free  by  electrolysis  are  still  further  simplified  by  using 
the  constants  in  Table  III;  it  being  then  a  physical 
as  distinguished  from  a  chemical  relation,  the  con- 
stants become  the  same  for  all  the  gaseous  elements, 
as  they  no  longer  involve  the  atomic  weights;  this 
follows  from  a  combination  of  the  laws  of  Faraday  and 
Avogadro.  This  relation  is  accurately  true  only  for 
perfect  gases;  slight  deviations  may  therefore  arise 
in  practice.  The  additional  basic  constant  involved 
in  the  determinations  of  the  conversion  factors  in  this 
Table  III  is  the  constant  of  Avogadro's  law,  namely 
22.390  liters,  for  the  volume  of  a  gram  molecule  of 
any  of  the  elements  in  their  gaseous  state,  at  0°  C  and 
760  mm.  This  constant  is  here  deduced  from  the 
weight  of  a  liter  of  oxygen  1.4292  grams1  and  its 
molecular  weight  32,  by  dividing  the  latter  by  the 
former.  The  other  basic  factor  is  that  in  these  six 
gaseous  elements  the  molecules  consist  of  two  atoms, 
that  is,  they  are  diatomic. 

The  application  of  the  constants  in  Tables  I  and 
EH  to  the  solution  of  practical  problems  is  described 
by  typical  examples  given  hi  Section  IV. 

1  This  value  is  the  one  used  in  the  well  known  Landolt- 
Boernstein  tables  as  the  basis  for  calculating  the  densities  of 


TABLES 

OF 

ELECTROCHEMICAL 

AND 

ELECTROPHYSICAL   EQUIVALENTS 

AND 

THEIR  DERIVATIVES 


12  ELECTROCHEMICAL   EQUIVALENTS 


« 


• 

il 


S 


ss 


,      OH 

JJllIj 


Sis 


fM    tO    O    U3      t- 
"•I    ^t    00    TH      rH 


00 

10    CO     ">  Of  *•«  £•  TH 

lO    C*     ^    lO    CO    O  OS 

co  T-i    \o  <N  TH  6  »d 


t~     (^ 

S  K 


7 
0.33702 


^    00     t^*    O) 
iH   O     *^   O 


10    CO 
O   O 


oo 

l^  CO  OS  «^ 

O5      <^>  CO  CO  t^ 

CO     °O  ^<  O  ^ 

O     cJ  «  rji  ^ 


oq  TIJ  q    •* 
co  co  os    TH 


CO 


O      ^^IJCfl      b«.CNTHTH      t» 

o    »^oc>    oiooo    o 


CO     »-<    CO   IO     *H    CO 


S 


co  co 

CO    CN       00 


TABLES  13 

TH    CO    0    O        CO       10        00       >OO  pt^  00    O    CO    T- 

10    TH  OO  <N    00   Ti<    C 

CNIO  CO^*  •¥  Cl  «H  G 

OO  CNCO  COOt-Tt 


rH<N       CO 


cq  co  O  ^      CD      1-1 

IQ    IO    CD    CO        T-H        0> 
rH    Tj<    t»   O        CN 


o  *  co     I     c$     I 


t~  r*<     w  T-J     "^  T~!  °?  o.     ^     °*.     °.     ^  °1     °Q°?     *^  °^  ^  "^ 

lOCO       OO       COCNrHO        ^       O        TH        OO       COCN        CN    O    O    O 


&OCO  iH 

C£>    ^  O 

CO    ^*  ^H 

coco  co 

oo  t- 


CO    ^P 

coo 


C)t«  O  00  00 

CDb*  O  iH  t> 

t*    ^*  I?*  ^5  CO 

toco  TJJ  CN  co 

i-icN  o  o  T* 


Tjiod     oo     oc4coid 


"*  ** 

CO    00        00    O)    O)    C9        O) 
''O       O»O»»OTj        O 


^        G)    O) 


i-        OO       CNOOO       Ol       •*!<       O       OO       rH 


O)    O)    LO    O) 

Cl    "^    CO    00 
«Tj|CNiH 

rHOOO 


r- 

CO       CO 


2O   O  CJ 

co  TH     S  S  ;H 

SCO    O        TH        CN        TH        C-    iO        cOtO  CN 

OTH        t-       t-       00       OrH       pt-:  t-; 

r-i  co  co  oo     TH     o     W 


TH    CO        COCN        CN    C^    O    TH 
C-T*        00        OOCNrHTH 


CO    CN    t- 
CO    iH    O 


II 


00       00       0000       O       TH       O       00       00       0000 


CO>O       COlO       rH 


C4       rH       CN 


q          S  §     5     5     § 

d     gi  g  g  §  si     § 


IO  <D 

CN  -«J 

10 

CO 


T3        W        03  0)  _ 

o    o    o    o        o        u 


S   I    g 

1 1 1 
3  <3  ^ 


•g    I 

o        o 


14  ELECTROCHEMICAL  EQUIVALENTS 


OO      C4       TH 


i-l      fr^    TH 


CN      d    IO    CO 

TH      vr>    (N    iH 


t>  (M  (M 
O  CO  iH 
i-JlOCO 
Tj<  T-i  •«* 


^ 


CO    C^l 

^H  co 


co    TH    co 

rH      TH      CO 


gO 
o 
^  t- 

9\CT) 


CO 


t^  oo     CN    oo 

COrH      O      O 


<\i  to 


CO   O^  ^    CO   C^      CO      O)   00      TJ* 

T-HCO^       >0    CO    CT>       CO       t-    10      TH 
rH    CO    CO      ^O    t*"    ^?      00      TH    OO      CO 


00    t-    IO    TH      VO    (N 


8 

TH          g§          * 


Tji     <M      10 


" 


QO  o  o  o    »i 

<*>    CO    t-    00      >-1 
*0    <N    TH    O      ^o 


b-     N. 

-*      VO 


O      IO    CN      CO      t» 
TH      CO    CO      10      10 


ooooooooooo 


HIO         ioi>qqcoq 
>oco         cit^ciosi>o> 

J5      CO  COCOIOTHIOCO 


O  ^^  >t|_id  i3oJ  0> 

O  Uu         QWP^feOO         O 


1s     I  ! 

II     1 1  I  II  •- 


•all! 
e<  •«  *o  .; 


o 


TABLES 


15 


2 


CDtOIO<^ 


*H  CM 


CN^  t-OOCOCOO\Tj<OO  i-l    CO     CO     Ci 

,Ht-0>0>C'iHO^COTHO<MTHqpt- 


S  10  C4    10 


Oi  CO 

00   r-J 

id  o 


t»  IO  O  CO        CO 
T*  t-  CN  CD  O  ^  10 


s 


oooc>rHiHo 


CN  S  00  I* 

o  o  co  o 


^ 


10     O>     THCO     CNOO^O     00     <aTHi-l     CO 

o    t,    ^^n    oq^rH    op    joco^j    03 


T-i    co    i-i 


S  (NO 

TH     t-    CN     00 


tO    CO     t^* 
CO    O)     ^H 


CO    CO    CO 

^cNiH 


CN  IO     00     00 

5     8  §  ^     § 

TH  TH      iH      fH  fH 


O>  rH     00 


»g 


3-3     w  w 


o  o 


II 


II 


16  ELECTROCHEMICAL  EQUIVALENTS 


CO    00    <N    •**<    C- 

CO    00    CO    10    C-  iH      »-i   C*    00 


»H      »/i    O    TH    00    CO    OO  t*  OOOOO 

<N      \0    <N    OS    to    <N    CO  t-;  VjCOtQ 

OS  OJ  bC    Tl< 

tO  to  O    i-H 


0>O      OrH      VOCOCJCp.COO?      CSI      t>^iH 


o  o  o  to 

oo  o  to  o> 

»-l  10  O  <M 

U5  Ol  IO  iH 


5§S 


to  co    o    co 


00 


00 


O       OOC~COtOC4i-IO      COCO       N.'    iO    CO    rH    OS    t^      tO 

o<i     Csdi-iiHoiooco    00     QJOOTHIHTH    d    Csdrn 


O  <N   (N   t^  to  CO 

coto  t.  ^coo 


t^  CO   f*5  r-i 


o  «  co 

"^  CO  O)   LQ 


OOK.OOOCO  OO^OO^ 

OS       ts.    IO    <N    p    IO    (N    O      "*    ^       ^    ^    R 

t-^    ^coidt^dcfl^    do    >«i«oo 


t-  oo  oo 

t-  (N  10 


iH      OS 
rH      00 


00  -^  CO 
00  T»<  CO 


o 

O      O\^ 


O      <2>OOOOOO     O?tH      C)OOOOO     O 


<N      CO 

CO       OS 

' 


o        o 


I 

^»  TI\ 


TABLES 

00      ^  t~    <*    rH     >0 


17 


O     *1   CO 

io^-* 
t-vo^ 

O     ")    >O 


r     •<  - 

<\l^OO«OC^ 

•^    00    CO      ^C    1-1    O 
•^    CO    (N      QOCOO 


<N 
rH   O     »-i   O 


38  §2SS  S 


doococJcoeooorH^oqioqqcooi         oo 
dtsicNr-idd^oi^ddod^oico        co 


OJ  O 


IO 

^< 


10     N      1/5    C- 

ddo'd 


CO   ^  t«»     t»   CO  O 

OO      <vJrHO      OO     rHO      »-i 


O      CO    rH    rH     rH  rH 


§      gg 
4     ^     ^    rH 


§ 


O     00     00    00 


G>^ 


ci 


S; 


r*    ^  *** 

QOCOOOIOOS^OOCOCO         coco 
*-it-co    Ss^j    oo^    VO<MCO    J5g^-« 

^   IO  t»   ^  O  CO   rH 
O  10  d   "5  rH  O   O 


S      S  rH  ^S 

IO      CO  rH  <V)  IO 

oo  t-  ~;  o 

Tjl  rH  V^  CO 


<2»OO 


OO     OO 


rH  O  0  0      O  T-l 


d^COrH  COdtMCO 


8 


8 


§  8 


o     2     ft 


d 

«  -o  o, 

bC  oj  to 

I  I  I 


•& 


18 


ELECTROCHEMICAL   EQUIVALENTS 


CO   O     t- 


\  $§£S 


T»<    O5 

882 

rH    10    CO 
CO   «O   ^ 


^-     10    oo    o 


CO    C-   00  CO  O    t-  »O 

<\iiococq  -^  ^  Tj<  t»  Tf  o> 

^°5S5!  P  S2  tSS  °2 

Os-^eot-  t-  ^  t-coo>  cp 


CO     00   CO 

(N     ON    O5 


COTjtlOrt' 

t»CO      TH      »O 
i-rH»OTH 


CO      t-      iH      CO      »O      <*OCO 
iHOT-CNTj«vsT-H 


»O      <*OCO 


»O      t- 
OCO 


S 


TjJ       1-J       C1 

g  ^  g 


«  S  8  8  $ 


tf> 


w   < 


C/D    C/3 


II 

11 

«    OS 


ill 

3  3  *• 

en  co  C/D 


I  ...  II 

.«    >   ^ 


2  g 
s   3 

CO    C/D    CO    CO 


TABLES 


19 


TH  CO  TP   TH   Ci  Ci  CO  O   iO  TH  CO   N.  IO  O  00  CO   *>  CN  CD  iH  LQ  CO 
P     ^   ,_,  »0  t-  CN      CO  f   <=>  <=>  TH  CO  CO  Ti   C>  TH  TH  CN  CN  CO 


T-i  CN    o    ci  od    ci    cd    Tj    c     i-     <>  CN  TJ< 
o  oo  c-    o    10  c-    o    TH    oo    TH    so  co  co 


o  oo 

TH    CO 


10     CN  TH     CN      CN     CN    -^      O  TH    CN    CO 


CO  t-  O  t~  t>  O    00  O  O 

t-  ^*i  oeo  oo  o»  »HO  o»  >*t- 

^  CO  t~O»  l>  vH  00    Tti  00  ^CO 

t-  CO  t-»0  t-  CO  OO-^  O>  »IO 


co 

OO 


O 

O> 


rH    ^<    cd  id    T}<    ^     ^<c     o 


co  nJ  oo  co 


VOCO 
^tH 


cOTHCOCD 
lO    TH    CO    rH 


OOTH  tO  rH^I  iH  t-  THC 

(N    TtH    tD  O  COO)  CO  t~  iO    O  CN  ^    Ci    00    CXI    t-  >"«(    CO    lO    CO    t- 

^CqtNj  10  iHCO  TlJ  rj|  ^*|O4  CN  *^tN»Ot-;CO  *»JCOT1JIOCO 

o  d  T-l  o  oo  o  o  oo  cs  o  o  o  o  o  o  o  o  o  o  o 


00  C5  t~-  TH  CO  CD  0>  TH  O  Tj«  ^O  CO  iH  t-  -^ 
T-Jf;  O  «O»0  TH  O  «T-|  -^  OOTpb-COTH 
T-i  O  TH  t^C4  <N  (N  (N  TH  O  VO  CO  TH  i-i  T-i 


CO  ^-  CO  00  CO   O)  O  00  tO    TH  ^  "^    00    t^   C9    CO  ^O    tO    O    to   CO   CO 

TH  (N  -^  TH  t^    TH  CO  TH  CNIO  CN  <9  V  0  H  V  <Sl    rH    CN    CN    CO    Tj< 

10  q  10  oq  •^I'^J  «o  t^  ^J0?  °.  ^x0.*^1^  ^^^J0.^!^ 

TH  CO  Tj<  TH  O    TH  TH  TH  TH    CO  00  <SrHCJC4CO  O*    T-i    TH    CN    C»    CO 


COCOCNtO              TH  TH  CO  C-    CO  <N  CO    (N    t-    TH  »O    T*    TH    CO 

CO    CO    CN      C1  TH    t-  TH  O  O    IO  CO  O^<b*COCO  'O    00    TH    b-    -^ 

OOO      O>  T}<    TJ4  CN  CN  tOt-  Tj*  SO    CO    CO    iH    t^  =C    CN    C^    CO    TH 

CO    CO    CN     ^  TH    O  CO  OO  TH    CO  CN  ^    tO    t^*    00    TH  VO    CN    TH    O>    TH 

OCOCN    to  T-jt-  eq  to  «oco  T-J  c>o>^coco  >>oo«o^j^j 

OOO    O  CN    O  O  O  OO  O  *•  O  O  O  O  (^OOOO 


CM    ^    CO     CO     iHCO     Tj«     CO 


^    CO    r^    IO    CO 


CN    q 

O     Tji 
IpQ 


^    10    t> 

CN     00     CO 


CN 


I 


B  § 

II 

s  I 


20 


ELECTROCHEMICAL  EQUIVALENTS 


t*    TH    IQ    C^      Ol      C^      O5      t*  .          •     ^^ 

cotdcoc<ic>T-iTHco          ^  2§  ~t; 
r>iHioo>    TH    T-I    t-    eoCxiS^ 

-«Ht-O>THO?THCOIO  rtNX 


O5    O>    rj<    CO      >O      CO      OO      CO^>C4>> 
OCOOCOt-TfCOOO  dC^v 

(NtHTHOTlicQNT-i  ^S' 


QC 


O      O     O      iH 


CO   Tt^    00    *^H  CO  x    ^^     ^ 

Q»>OCOt«COtOOTHT)<  ^CO^ 

o\O)co^cotHT-ic4co  CqX 
*»ioooc>    oi    i-i    T-I    o 


COtOTHCOCqOiCN  ^Tj*^ 

•*  C    CO     > 

o> 


CO    IO    t-    O      T-4      CO 


•^St-OOCOTHtOiHCOCO  ^COX 

^5CMiHT-lt-      CO      Tj(      t-      t-\CO^, 

^cqiHT-jTHtococooq         flqX 
cjooo'd    o    o    o    d 


^«COTt«lO      CO     CO     C*      rJI>X 


CO 


t-      CO     <O 

§  s  § 


11 ,1 

SF   3*   M   a 

>H       >H       N       N 


04 j    3     g    ^    « 

§  ^>  5  g  gjj 

P  6  M  ^ 


I  fill 
Illll 


o  o 


O 


.I 

It'll 


Table  H 

GRAMS    PER    AMPERE-HOUR 
or  Kilograms  per  1000  Ampere-hours  (Column  7  of  Table  I). 

IN  ORDER  OF  MAGNITUDE 
(Values  which  are  in  italics  in  Table  I  have  been  omitted  here.) 


val. 

val. 

Hydrogen 

1 

0.037607 

Scandium 

3 

0.54843 

Boron 

5 

0.082078 

Arsenic 

5 

0.55932 

Nitrogen 

5 

0.10454 

Bromine 

5 

0.59633 

Carbon 

4 

0.11197 

Molybdenum 

6 

0.59693 

Boron 

3 

0.13680 

Sulfur 

2 

0.59805 

Oxygen 

4 

0.14923 

Ruthenium 

6 

0.63237 

Glucinum 

2 

0.16975 

Vanadium 

3 

0.63424 

Nitrogen 

3 

0.17423 

Chromium 

3 

0.64667 

Chlorine 

7 

0.18899 

Germanium 

4 

0.67621 

Sulfur 

6 

0.19935 

Iodine 

7 

0.67645 

Carbon 

2 

0.22394 

Manganese 

3 

0.68311 

Phosphorus 

5 

0.23161 

Iron 

3 

0.69443 

Manganese 

8 

0.25617 

Columbium 

5 

0.69766 

Lithium 

1 

0.25892 

Fluorine 

1 

0.70885 

Silicon 

4 

0.26395 

Molybdenum 

5 

0.71632 

Chlorine 

5 

0.26459 

Nickel 

3 

0.72975 

Manganese 

7 

0.29276 

Cobalt 

3 

0.73335 

Oxygen 

2 

0.29847 

Selenium 

4 

0.73870 

Sulfur 

4 

0.29903 

Calcium 

2 

0.74747 

Chromium 

6 

0.32334 

Tellurium 

6 

0.79280 

Aluminum 

3 

0.33702 

Zirconium 

4 

0.84503 

Manganese 

6 

0.34156 

Sodium 

1 

0.85809 

Vanadium 

5 

0.38054 

Gallium 

3 

0.86928 

Phosphorus 

3 

0.38601 

Osmium   - 

8 

0.89027 

Arsenic 

7 

0.39952 

Molybdenum 

4 

0.89540 

Bromine 

7 

0.42595 

Antimony 

5 

0.89689 

Chlorine 

3 

0.44098 

Arsenic 

3 

0.93221 

Titanium 

4 

0.44863 

Iodine 

5 

0.94703 

Magnesium 

2 

0.45367 

Ruthenium 

4 

0.94856 

Ruthenium 

8 

0.47428 

Vanadium 

2 

0.95136 

Vanadium 

4 

0.47568 

Chromium 

2 

0.97001 

Selenium 

6 

0.49247 

Bromine 

3 

0.99389 

Manganese 

4 

0.51234 

Palladium 

4 

0.99520 

21 


22 


ELECTROCHEMICAL  EQUIVALENTS 


val. 

val. 

Manganese 

2 

1.0247 

Samarium 

3 

1.8704 

Iron 

2 

1.0416 

Europium 

3 

1.8903 

Nickel 

2 

1.0946 

Lead 

4 

1.9326 

Cobalt 

2 

1.1000 

Gadolinium 

3 

1.9562 

Yttrium 

3 

1.1031 

Terbium 

3 

1.9798 

Tin 

4 

1.1071 

Palladium 

2 

1.9904 

Uranium 

8 

1.1109 

Dysprosium 

3 

2.0209 

Tungsten 

6 

1.1441 

Holmium 

3 

2.0333 

Copper 

2 

1.1858 

Erbium 

3 

2.0855 

Osmium 

6 

1.1870 

Thulium 

3 

2.0955 

Tellurium 

4 

1.1892 

Cadmium 

2 

2.0967 

Molybdenum 

3 

1.1939 

Indium 

2 

2.1415 

Platinum 

6 

1.2138 

Ytterbium 

3 

2.1577 

Zinc 

2 

1.2194 

Thorium 

4 

2.1676 

Rhodium 

3 

1.2797 

Lutecium 

3 

2.1763 

Gallium 

2 

1.3039 

Tin 

2 

2.2142 

Cerium 

4 

1.3081 

Uranium 

4 

2.2217 

Chlorine 

1 

1.3229 

Copper 

1 

2.3717 

Tantalum 

5 

1.3543 

Tellurium 

2 

2.3784 

Tungsten 

5 

1.3729 

Gold 

3 

2.4524 

Indium 

3 

1.4277 

Thallium 

3 

2.5370 

Potassium 

1 

1.4588 

Barium 

2 

2.5625 

Selenium 

2 

1.4774 

Bismuth 

3 

2.5867 

Uranium 

6 

1.4811 

Uranium 

3 

2.9623 

Antimony 

3 

1.4948 

Bromine 

1 

2.9817 

Bismuth 

5 

1.5520 

Rubidium 

1 

3.1880 

Iodine 

3 

1.5784 

Tungsten 

2 

3.4323 

Strontium 

2 

1.6347 

Platinum 

2 

3.6413 

Tungsten 

4 

1.7162 

Mercury 

2 

3.7420 

Lanthanum 

3 

1.7286 

Lead 

2 

3.8651 

Cerium 

3 

1.7442 

Silver 

1 

4.0248 

Praseodymium 

3 

1.7522 

Radium 

2 

4.2158 

Uranium 

5 

1.7774 

Iodine 

1 

4.7351 

Molybdenum 

2 

1.7908 

Caesium 

1 

4.9549 

Neodymium 

3 

1.7945 

Gold 

1 

7.3572 

Iridium 

4 

1.8011 

Mercury 

1 

7.4840 

Platinum 

4 

1.8206 

Thallium 

1 

7.6109 

Table  m 

ELECTROPHYSICAL  EQUIVALENTS  OF  GASES 
BY  VOLUME 

The  following  constants,  which  are  independent  of  the  atomic 
weights  or  vapor  densities,  apply  to  all  the  six  elements,  BRO- 
MINE, CHLORINE,  FLUORINE,  HYDROGEN,  NITROGEN, 
and  OXYGEN,  which  in  their  free  state  are  normally  gases, 
and  all  of  which  are  diatomic.  They  are  here  assumed  to 
have  the  properties  of  a  perfect  or  ideal  gas.  The  constants 
are  for  a  unit  change  of. valence,  hence  for  any  other  change 
of  valence  (for  oxygen  it  is  generally  2)  the  constants  of  the 
first  group  must  be  multiplied  by  it  and  those  of  the  second 
group  divided  by  it. 

The  volumes  of  the  gases  are  for  0°  C  and  760  mm, 

8.6193  coulombs  per  cubic  centimeter ; 
2.3943  ampere-hours  per  liter ; 
67.798     ampere-hours  per  cubic  foot 

The  reciprocals  are : 

0.11602  cubic  centimeter  per  coulomb ; 
0.41767  liter  per  ampere-hour: 
14.750      cubic  feet  per  1000  ampere-hours. 


23 


Table  IV 

VALENCES   OF  THE  ELEMENTS  IN  THEIR 
COMBINATIONS 

Prepared  by  Prof.  Jos.  W.  Richards 

The  following  are  the  practical  or  actual  valences  irrespective 
of  any  interpretation  involving  structural  formulas.  There  are 
additional  valences  which  occur  more  rarely,  and  still  others 
about  which  there  may  be  some  doubt.  By  the  word  "  salts  " 
is  meant  oxides,  sulfides,  sulfates,  chlorides,  chlorates,  etc. 

NAMES  VALENCES 

Aluminum Salts    +  III;    aluminates  +  III. 

Antimony Antimonous  salts  +  III ;    antimonic  salts  +  V ; 

antimonites  +  III ;    antimonates  +  V ;    anti- 

monides  -  III,  sometimes  -  I  and  -  II. 

Argon Non-valent ;  forms  no  known  combinations. 

Arsenic    Arsenious  salts  +  III ;   arsenic  salts  +  V ;  arse- 

nites  +  III ;  arsenates  +  V ;  arsenides  -  III, 

sometimes  -  I  and  -  n. 

Barium Salts  +  II ;  peroxide  +  IV. 

Bismuth Bismuthous  salts  +  III ;    bismuthic  salts  and 

bismuthates  +  V. 

Boron Salts  +  III ;  borates  +  III ;  perborates  +  V. 

Bromine Bromides  -  I;    hypo-bromites  +  I;     bromites 

+  III ;  bromates  +  V ;  .perbromates  +  VII. 

Cadmium Salts  +  H. 

Caesium Salts  +  I. 

Calcium Salts  +  H. 

Carbon Carbonates  +  IV ;    salts  usually  +  IV ;    in  CO 

+  II ;  hydrocarbons,  free  valences  -  I  to  -  IV. 

Cerium    Cerous  salts  +  III ;   eerie  salts  +  IV. 

Chlorine Chlorides    -  I ;     hypochlorites    +  I ;    chlorites 

+  III;  chlorates  +  V;  perchlorates  +  VII;    in 

chlorine  oxides  + 1,  +  III,  -f  IV,  +  V,  +  VII. 
24 


TABLES 


25 


Chromium Chromous  salts  +  n ;  chromic  salts  +  HI ;  tri- 

*  oxide  +  VI ;   chromites  -f  ni ;   chromates  or 

di-chromates  +  VI. 

Cobalt   Cobaltous  salts  +  H ;  cobaltic  salts  +  HI. 

Columbium CbO   +  H ;    CbO2   +  IV ;    columbic  salts  and 

columbates  +V. 

Copper Cuprous  salts  +  I ;   cupric  salts  +  n. 

Dysprosium  ....  Salts  +  III. 

Erbium Salts  +  m. 

Europium Salts  -f  HI. 

Fluorine Fluorides  -  I ;  all  compounds  -  I. 

Gadolinium Salts  +  in. 

Gallium Salts  +  HI. 

Germanium  ....  Germanous  salts  +  n ;    germanic  salts  +  IV ; 

germanites  +  n ;    germanates  +  IV. 

Glucinum Salts  +  n. 

Gold Aurous  salts  + 1 ;    auric  salts  +  HI ;    aurates 

+  m. 

Helium Non-valent;  forms  no  known  combinations. 

Holmium Salts  +  HI. 

Hydrogen   +  I ;  in  peroxide  +  H. 

Indium Salts  +  m. 

Iodine    . . Iodides   -  I ;    hypo-iodites  +  I ;  iodites  +  in ; 

iodates  +  V ;  per-iodates  +  VH ;   iodic  oxide 

+  V. 

Indium Iridous  salts  +  HI ;  iridic  salts  +  IV. 

Iron   Ferrous  .salts  +  H;   ferric  salts  +  HI;   ferrites 

+  HI ;  ferrates  +  VI. 

Krypton Non-valent ;  forms  no  known  combinations. 

Lanthanum Salts  +  HI. 

Lead Usual  salts  or  plumbic  salts  +  H ;   di-oxide  or 

peroxide  and  plumbates  +  IV ;  sub-oxide  +  I. 

Lithium Salts  +  L 

Lutecium Salts  +  HI. 

Magnesium    .  .  .  Salts  +  H. 

Manganese  ....  Manganous  salts  +  H ;    manganic  salts  +  HI ; 

di-oxide  or  peroxide  +  IV ;  manganates  +  VI ; 

permanganates  -f  VH. 

Mercury Mercurous  salts  +  I ;  mercuric  salts  -f  H. 

Molybdenum    . .  Molybdous  salts  +  H ;  molybdic  salts  -f  HI ;  di- 
oxide +  IV ;  tri-oxide  and  molybdates  +  VI. 
Neodymium   .  .  .  Salts  +  HI. 


26  ELECTROCHEMICAL  EQUIVALENTS 

Neon   Non-valent ;   forms  no  known  combinations. 

Nickel   Nickelous  salts  +  II ;  nickelic  salts  +  III. 

Niton Non-valent;  forms  no  known  combinations. 

Nitrogen    Ammonia   and    ammonium   salts    (NH4   salts) 

-  Ill ;     most    organic    nitrogen    compounds 

-  Ill ;    nitrous  oxide  +  I ;    nitric  oxide  +  II ; 
sesqui-oxide  and  nitrites  +  III ;  di-oxide  (per- 
oxide)  +  IV ;    nitric  anhydride  and  nitrates 
+  V.     (In  ammonium  nitrite  and  nitrate  the 
N  in  the  NH4  radical  is  -  III  and  in  the  acid 
radical  +  III  or  +  V.) 

Osmium Osmous  salts  +  II ;  osmic  salts  +  IV ;  sesqui- 
oxide  +  III ;  tri-oxide  and  osmates  +  VI ; 
peroxide  and  perosmates  +  VIII. 

Oxygen   Oxides,  salts,  etc.  -  II. 

Palladium Palladous  salts  +  II ;  palladic  salts  +  IV. 

Phosphorus  ....  Phosphorous  salts  and  phosphites  +  III ;  phos- 
phoric salts  and  phosphates  +  V ;  phosphides 

-  Ill ;    hypophosphites  +  I ;    hypophosphates 
+  IV. 

Platinum Platinous   salts   and   platinites   +  II;    platinic 

salts  and  platinates  +  IV. 

Potassium Salts  +  I. 

Praseodymium . .  Salts  +  III. 

Radium Salts  +  II. 

Rhodium Rhodous      salts  +  II ;     rhodic      salts   +   III ; 

dioxide  +  IV. 

Rubidium  Salts  +  I. 

Ruthenium Ruthenous   salts   +  II ;    ruthenic   salts   +  III ; 

ruthenic    anhydride    and    ruthenates    +  VI ; 

per-ruthenic  anhydride  +  VIII. 

Samarium Salts  +  III. 

Scandium   Salts  +  III. 

Selenium Selenites  +  IV ;   selenates  +  VI ;  selenides  -  II. 

Silicon Silicides  -  IV;   salts,  oxide  and  silicates  +  IV. 

Silver Salts  +  I. 

Sodium .  Salts  +  I. 

Strontium Salts  +  II. 

Sulfur Sulfides  -  II;   di-sulfides  -  I;  SO2  and  sulfites 

+  IV;    SO3  and  sulfates  +  VI;    hyposulfites 

(thio-sulfates)   +11;    S2O3  +III;    S2O7  and 

per-sulfates  +  VII. 


TABLES  27 

Tantalum Salts  and  tantalates  +  V. 

Tellurium Tellurides    -  n ;     di-tellurides    -I ;     tellurous 

salts  +  n ;  telluric  salts  and  tellurites  +  IV ; 

TeO8  and  tellurates  +  VL 

terbium Salts  +  HI. 

Thallium Thallous  salts  + 1;  thallic  salts  +  ffl. 

Thorium Salts  +  IV. 

Thulium Salts  +  HL 

Tin Stannous  salts  and  stannites  +  H ;  stannic  salts 

and  stannates  +  IV. 
Titanium Titanous  salts  and  titanites  +  ffl;  titanic  salts 

and  titanates  +  IV. 
Tungsten WO  +H;    WO2  and  WCU  +IV;    WCU  +V; 

tungstic  oxide  and  tungstates  +  VL 
Uranium   Uranous  salts  +  IV ;  uranic  salts  and  uranates 

+  VI;     oxides    +m,    +IV,    +VI,    +VHI; 

chloride  +V. 
Vanadium Vanadates   +  V;    vanadous   salts   +  HI;    VO 

+  H;  V02+IV. 

Xenon   Non-valent ;  forms  no  known  combinations. 

Ytterbium Salts  +  m. 

Yttrium Salts  +  HI. 

Zinc Salts  +H. 

Zirconium. .      . . Salts  and  zirconates  +  IV. 


Section   IV 

CALCULATIONS   INVOLVING  ELECTROCHEMICAL 
EQUIVALENTS.     EXAMPLES 

There  are  in  general  three  ways  of  making  calcula- 
tions which  are  based  on  Faraday's  law  and  there- 
fore involve  electrochemical  equivalents,  that  is, 
calculations  of  the  quantities  of  the  materials  by 
weight  which  are  deposited,  dissolved,  or  otherwise 
chemically  changed  when  an  electric  current  is  passed 
thru  an  electrolyte.  The  simplest  cases  are  so  easy 
to  calculate  with  the  aid  of  the  accompanying  table 
that  very  little  and  in  some  cases  no  knowledge  of 
chemistry  is  required ;  even  in  some  of  these  simplest 
ones,  however,  it  is  essential  to  know  what  the  so- 
called  "valence"  is  of  the  chemical  element  in  the 
problem;  whenever  it  is  unity  it  can  be  neglected; 
those  who  do  not  know  how  to  determine  it  had 
better  consult  a  chemist ;  an  explanation  of  the 
meaning  of  this  term  is  given  in  Appendix  I.  In  the 
more  involved  cases  a  knowledge  of  chemistry  is 
required  for  making  the  calculations ;  some  of  the 
elementary  principles  of  chemistry  are  given  in  Ap- 
pendix II. 

The  first  and  simplest  method  of  making  such 
calculations  is  to  use  the  figures  given  in  Table  I, 
which  includes  all  the  elements  and  practically  all  the 
valences  occurring  in  practice ;  all  that  is  necessary 
then  is  to  multiply  the  proper  figure  from  the  table 
(being  careful  about  the  valence)  by  the  quantity  of 

28 


EXAMPLES  29 

material  or  current  and  the  time  stated  hi  the  par- 
ticular problem ;  the  table  saves  the  most  tedious 
parts  of  the  complete  calculations,  as  they  have 
already  been  made  in  calculating  the  values  given  in 
it ;  the  table  is  a  convenience  but  not  a  necessity,  as 
the  calculations  could  all  be  made  without  it,  tho  they 
are  then  more  laborious  and  sometimes  far  more  so. 

The  second  method  is  based  on  the  single  electro- 
chemical constant  called  a  "faraday"  which  is  the 
same  for  all  the  elements.-  It  is  the  electric  charge 
carried  by  a  gram  ion  when  the  valence  is  unity.  No 
table  is  then  required,  but  the  calculations  are  often 
quite  lengthy,  tedious,  and  confusing.  It  is  then 
necessary  to  know  the  value  of  the  faraday ;  its  best 
known  value  at  the  present  time  is  very  nearly  96,500 
coulombs  or  about  26.80  ampere-hours  (more  ac- 
curately 96,493.7  and  26.8038).  As  before,  it  must  be 
known  what  the  valence  is  in  the  particular  problem. 
For  valences  2,  3,  4,  etc.  (whether  positive  or  nega- 
tive), the  charges  are  2,  3,  4,  etc.  faradays. 

When  the  elements  are  set  free  in  the  form  of 
gases  or  vapors,  and  when  the  amounts  are  desired 
hi  terms  of  their  volumes  instead  of  their  weights, 
there  exists  a  still  simpler  constant  than  the  faraday, 
because  the  amount  of  electricity  required  to  set  free 
a  liter  of  the  vapor  of  any  element  is  always  the  same 
per  unit  atom  in  the  molecule  and  per  unit  change  of 
valence.  This  constant  for  0°  and  760  mm.  is  4309.7 
coulombs  or  1.1971  ampere-hours  per  liter.  This 
need  then  merely  be  multiplied  by  the  number  of 
atoms  in  a  molecule  of  the  gas  or  vapor,  called  its 
atomicity  (and  apparently  always  a  simple  whole 
number),  and  by  the  change  of  valence  (also  generally 
a  simple  whole  number)  to  give  the  result  directly. 
For  the  atomicity  of  an  element  works  on  chemistry 


30  ELECTROCHEMICAL  EQUIVALENTS 

should  be  consulted.  The  change  of  valence  must  be 
determined  hi  each  particular  case ;  hi  all  ordinary 
cases  that  of  hydrogen  is  1  and  of  oxygen  2.  For  the 
six  gaseous  elements,  the  atomicity  of  all  of  which  at 
ordinary  temperatures  is  2,  this  constant  and  its 
derivations  are  given  hi  Table  III.  As  the  calcula- 
tions are  then  so  simple  and  direct  no  further  explana- 
tions are  necessary  (see  Example  2  below). 

The  third  general  method  of  making  electrochemical 
calculations  is  first  to  make  the  electrochemical  part 
of  it  for  some  other  convenient  element  or  radical, 
like  hydrogen,  oxygen,  zinc,  SO4,  or  some  element  in 
the  particular  reaction  for  which  the  calculation  is 
simple  and  surely  correct,  and  then  by  a  purely 
chemical  calculation  determine  what  the  chemical 
equivalent  of  this  amount  of  the  intermediary  element 
is  hi  terms  of  the  one  for  which  the  figures  are  de- 
sired. When  the  valences  of  the  two  are  the  same, 
then*  chemical  equivalent  weights  are  in  proportion  to 
their  atomic  weights ;  when  the  valences  are  different 
reduce  the  relative  weights  to  unity  valence  by 
dividing  the  atomic  weights  by  the  respective  valences. 
This  methods  always  requires  some  knowledge  of 
chemistry  and  sometimes  considerable.  In  some  of 
the  more  involved,  complicated,  or  obscure  cases  this 
is  the  safest  and  surest  method,  as  it  is  less  liable  to 
be  confusing.  It  is  always  more  lengthy  and  tedious 
than  the  first  method,  and  sometimes  much  more  so. 
If  hydrogen  is  always  used  as  this  intermediary  (be- 
cause its  atomic  weight  is  practically  unity)  the  table 
is  rendered  unnecessary  except  for  the  values  for 
hydrogen. 

With  these  brief  statements  about  the  three 
methods  they  are  best  explained  hi  detail  by  the 
following  set  of  examples  and  the  remarks  accom- 


EXAMPLES  31 

panying  them.  These  examples  have  been  chosen  to 
be  characteristic  of  the  more  usual  typical  cases  and 
include  also  a  few  of  the  unusual  ones. 

Example  I.  Simplest  case.  Valence  may  be  neglected. 
How  much  silver  will  be  deposited  per  hour  by 
10  amperes?  The  valence  of  silver  being  always 
unity  can  be  neglected.  For  silver,  column  7  of  the 
table  states  that  one  ampere-hour  will  deposit  4.025 
grams,  hence  10  amperes  will  deposit  40.25  grams  per 
hour  (one  troy  ounce  is  equal  to  20  pennyweight  or 
to  31.104  grams). 

To  calculate  this  by  the  second  method,  without 
the  table,  one  must  know  that  every  gram  ion  of  the 
silver  (or  of  any  other  element  whose  valence  is 
unity)  carries  a  charge  of  one  "faraday"  which  is 
equal  to  about  96,500  (accurately  96,493.7)  coulombs 
of  electricity  (a  coulomb  is  equal  to  an  ampere  flowing 
for  one  second).  In  cases  occurring  in  practice  it  is 
often  more  convenient  to  use  its  equivalent  26.8038 
ampere-hours.  A  gram  ion  of  silver  is  as  many  grams 
as  are  expressed  by  its  atomic  weight,  hence  for  silver 
the  weight  of  a  gram  ion  is  107.88  grams.  10  amperes 
for  one  hour  are  equal  to  10  x  3600  seconds  =  36,000 
coulombs  (or  ampere-seconds).  Dividing  this  by  the 
faraday,  96,500  coulombs  gives  0.373  gram  ions,  and 
as  a  gram  ion  of  silver  weighs  107.88  grams,  the 
desired  result  is  0.373  x  107.88  =  40.25  grams,  as 
before.  Or  the  faraday  may  in  this  case  be  more 
conveniently  taken  as  26.8  ampere-hours,  then  10 
ampere-hours  divided  by  26.8  equals  0.373  gram  ions, 
as  before.  The  use  of  the  table  saves  these  some- 
what lengthy  computations  and  the  errors  arising  in 
multiplying  when  one  should  have  divided,  or  the 
reverse,  as  the  problems  are  often  the  reverse  of  the 
present  one. 


32  ELECTROCHEMICAL  EQUIVALENTS 

In  the  third  method  of  making  this  calculation, 
which  may  be  resorted  to  by  those  who  are  not  used 
to  the  conception  of  valences,  or  hi  some  complicated 
or  involved  cases,  select  some  other  convenient  inter- 
mediary element,  like  hydrogen  for  instance,  for  the 
electrochemical  part  of  the  calculation,  using  the 
values  for  that  element  in  the  table,  and  then  by  a 
purely  chemical  calculation  determine  the  chemically 
equivalent  weights  of  that  intermediary  element  and 
of  the  original  one ;  the  electrochemical  equivalents 
will  then  be  hi  the  proportion  of  these  weights. 

In  many  cases  hydrogen  is  selected  as  this  inter- 
mediary element,  chiefly  because  its  atomic  weight  is 
practically  unity,  hence  the  corresponding  weights  of 
all  the  other  elements  are  equal  to  then*  atomic 
weights  which  must  however  be  divided  by  the 
valence  which  they  have  hi  that  particular  problem 
when  it  is  not  unity.  Another  reason  for  selecting 
hydrogen  is  that  the  whole  table  is  then  reduced  to 
the  few  figures  for  hydrogen  alone.  Hence  selecting 
hydrogen  hi  the  present  problem,  find  from  the  table 
how  much  hydrogen  will  be  set  free  in  one  hour  by 
the  10  amperes;  the  table  gives  0.03761  grams  for 
one  ampere,  hence  multiplying  by  10  gives  0.3761 
grams. 

To  find  the  chemically  equivalent  weights  of  silver 
and  hydrogen,  it  is  hi  this  case  sufficient  (because 
both  have  a  valence  of  unity)  to  use  their  atomic 
weights  107.88  and  1.008;  for  most  purposes  it  is 
accurate  enough  to  assume  that  of  hydrogen  to  be 
unity.  The  valence  of  silver  and  hydrogen  are  both 
unity  and  may  therefore  here  be  neglected ;  if  instead 
of  silver  it  were  zinc,  for  instance,  whose  valence  is 
always  2,  the  atomic  weight  of  zinc,  65.37,  would  have 
to  be  divided  by  this  valence  2  to  get  the  chemically 


EXAMPLES  33 

equivalent  weights,  which  would  then  be  32.69  and 
1.008. 

Having  found  the  chemically  equivalent  weight  of 
silver  to  be  107.88  +  1.008  =  107.02  times  that  of 
hydrogen,  multiply  the  above  0.3761  grams  of  hydro- 
gen by  107.02,  giving  as  before  40.25  grams  of  silver 
per  hour,  for  10  amperes. 

While  this  method  is  a  somewhat  involved  one  for 
such  a  simple  case  as  the  present  one,  it  is  explained 
here  because  it  is  often  a  safe  method  to  resort  to 
(even  if  only  as  a  check)  in  the  more  complicated  and 
involved  cases  like  those  in  which  there  is  no  deposit 
or  merely  a  change  of  valence,  as  is  the  case  for 
instance  with  depolarizers,  or  when  the  valence  is  not 
known  or  is  obscured ;  and  in  some  of  these  more 
involved  cases  it  may  be  more  convenient  to  use  some 
other  element  which  is  actually  involved  in  the  par- 
ticular reaction,  instead  of  hydrogen ;  these  cases  will 
be  described  below  in  other  examples. 

Example  2.  Gas.  How  many  amperes  will  it  take  to 
generate  a  cubic  foot  of  hydrogen  per  hour?  A  liter 
of  hydrogen  at  0°C.  and  760  mm.  weighs  0.09004 
grams,  hence  a  cubic  foot  will  weigh  0.09004  x  28.32 
=  2.55  grams.  The  valence  of  hydrogen,  being  unity, 
can  be  neglected.  From  Table  I,  column  8,  it  takes 
26.59  ampere-hours  to  generate  one  gram;  hence 
2.55  grams  will  require  26.59  x  2.55  =  67.8  ampere- 
hours  ;  therefore  it  will  take  67.8  amperes  to  generate 
one  cubic  foot  of  hydrogen  per  hour. 

Hydrogen  being  a  gas  and  as  the  amount  is  here 
required  in  terms  of  volume  and  not  of  weight,  this 
same  result  can  be  obtained  directly  from  Table  m. 

Example  3.  Anode.  Valence  2.  How  long  will  10 
pounds  of  copper  anodes  last  in  a  copper  plating  or 
electrotyping  bath  in  which  the  average  current  is  50 


34  ELECTROCHEMICAL  EQUIVALENTS 

amperes,  the  solution  being  a  cupric  salt,  like  sulfate 
of  copper?  The  valence  of  copper  in  a  cupric  salt  is 
2,  hence  from  the  table,  column  10,  one  pound  of 
copper  at  this  valence  will  be  consumed  by  382.5 
ampere-hours,  which  at  50  amperes  means  a  little 
over  76  hours. 

In  making  this  calculation  by  means  of  the  unit 
faraday,  it  must  be  remembered  that  the  copper  in 
this  case  has  a  valence  of  2,  hence  each  gram  ion  of 
63.57  grams  now  carries  a  charge  of  2  faradays  or 
193,000  coulombs.  50  amperes  equal  180,000  cou- 
lombs per  hour,  which  divided  into  193,000  gives 
1.072  gram  ions  of  63.57  grams,  making  68.15  grams 
or  0.150  Ibs.,  hence  10  Ibs.  will  last  76  hours,  as 
before. 

In  making  the  calculation  by  the  other  method 
based  on  hydrogen  as  an  intermediary  element  it 
must  not  be  forgotten  that  the  equivalent  weight  of 
copper  is  now  the  atomic  weight  divided  by  2,  because 
the  valence  now  is  2. 

Example  4.  Primary  lattery.  How  many  pounds 
of  zinc  will  be  consumed  per  hour  (not  including  local 
action)  in  a  battery  of  primary  cells  generating  1 
kilowatt,  the  available  voltage  being  1.7  per  cell? 
Zinc  always  has  the  same  valence,  2 ;  when  the 
figures  in  the  table  are  used  this  valence  has  already 
been  included  in  them  and  therefore  the  valence  may 
be  ignored  in  the  subsequent  calculations.  For  ziric, 
column  9  gives  the  constant  2.688  and  states  that 
when  divided  by  the  volts  this  is  equal  to  the  pounds 
per  kilowatt-hour.  Dividing  2.688  by  1.7  gives  1.58 
pounds  per  hour  for  one  kilowatt.  The  zinc  con- 
sumption will  of  course  be  the  same  for  a  single  large 
cell  as  for  a  battery  of  cells,  and  is  independent  of 
whether  the  cells  are  connected  in  series  or  in  parallel. 


EXAMPLES  35 

To  calculate  this  zinc  consumption  from  the  unit 
"faraday,"  that  is,  without  the  table,  the  valence  2 
must  be  taken  into  account.  This  unit  is  the  charge 
carried  by  a  monovalent  gram  ion,  that  is,  it  is  for  a 
valence  1.  For  any  other  valence  this  constant  must 
be  multiplied  by  the  valence ;  hence  for  zinc  it  is 
96,500  x  2  =  193,000  coulombs.  One  kilowatt  at  1.7 
volts  means  588  amperes  which  for  one  hour  is  equal 
to  3600  x  588  =  2,116,800  coulombs ;  dividing  by  2 
faradays  or  193,000  coulombs,  gives  10.96  gram  ions 
of  zinc,  and  as  one  gram  ion  is  numerically  equal  to 
the  atomic  weight,  hence  is  65.37  grams,  this  equals 
10.96  x  65.37  =  716.0  grams  ;  multiplying  by  0.002205 
gives  1.58  pounds,  as  before.  This  example  again 
shows  how  much  calculation  is  saved  by  using  the 
table. 

Single  valence.  The  above  examples  show  how  to 
use  the  table  when  the  chemical  element  is  set  free  or 
dissolved  and  has  only  a  single  valence,  in  which 
cases  there  can  be  no  question  as  to  what  the  valence 
is.  The  table  is  used  in  the  same  way  with  those 
elements  which  have  several  valences,  as  stated  in 
column  4 ;  it  is  then  of  course  of  the  utmost  import- 
ance to  know  which  of  its  valences  is  the  one  involved 
in  the  particular  problem ;  the  importance  of  this  is 
shown  in  the  next  paragraph. 

Several  valences.  When  copper,  for  instance,  is 
deposited  from  the  ordinary  copper  sulfate,  CuSO4 
(cupric  sulfate),  its  valence  is  2,  as  the  copper  then 
is  the  chemical  equivalent  of  two  atoms  of  hydrogen 
in  the  corresponding  hydrogen  compound  H2SO4 
(sulfuric  acid).  Hence  with  that  electrolyte  the 
constants  in  the  table  for  the  valence  2  must  be  used. 
If  however  it  is  deposited  from  the  cuprous  sulfate 
Cu2SO4,  the  copper  is  the  direct  equivalent  of  the 


36  ELECTROCHEMICAL  EQUIVALENTS 

hydrogen,  hence  its  valence  then  is  1.  As  will  be 
seen  from  the  table,  the  same  current  then  deposits 
twice  as  much  copper,  hence  the  importance  of  using 
the  constants  for  the  correct  valence. 

When  the  table  is  not  used,  or  only  indirectly,  the 
changes  necessary  in  the  calculations  when  the  val- 
ence is  anything  else  than  unity,  have  already  been 
described  above  hi  examples  1,  3,  and  4. 

Change  of  valence.  The  above  cases  are  the  more 
usual  ones  in  which  some  chemical  element  like  a 
metal  or  gas  is  set  free  or  dissolved  at  the  electrodes. 
In  some  other  cases  however  the  element  is  neither 
set  free  nor  dissolved ;  in  these  the  current  merely 
changes  the  valence  of  the  element  from  one  value  to 
another.  This  is  the  case  for  instance  in  many  of 
the  so-called  depolarizers  of  batteries,  like  in  the 
manganese  of  the  peroxide  in  the  usual  dry  cell,  the 
lead  of  the  positive  plate  of  the  lead  storage  battery, 
the  chromium  or  nitrogen  of  the  corresponding  acids 
in  the  Grove  or  the  Bunsen  cells.  Also  in  such  reac- 
tions as  the  changing  of  ferrous  into  ferric  salts, 
cuprous  to  cupric  salts,  etc.,  or  the  reverse. 

In  all  such  cases  the  simplest  rule  is  to  find  out 
what  the  valences  are  before  and  after  the  passage 
of  the  current,  the  difference  between  them  will  then 
be  the  change  of  valence,  and  it  is  this  difference 
which  must  be  used  in  column  4  of  the  table  to  find 
the  corresponding  electrochemical  equivalents.  The 
function  of  the  current  may  be  said  to  be  the  changing 
of  the  valence  of  an  element ;  and  for  a  unit  amount 
of  any  given  element  a  certain  definite  amount  of 
electricity  is  required  to  change  the  valence  by  one 
unit,  no  matter  whether  that  valence  was  high  or  low ; 
for  instance,  it  takes  just  as  much  electricity  to 
reduce  a  gram  of  copper  from  a  cupric  (valence  2)  to 


EXAMPLES  37 

a  cuprous  (valence  1)  salt,  in  which  operation  the 
change  of  valence  is  1,  as  it  does  to  deposit  a  gram 
of  the  metal  from  the  cuprous  salt  in  which  the  change 
of  valence  is  also  1 ;  after  metals  or  other  elements 
have  been  set  free  as  such,  their  valence  is  zero,  as 
they  are  then  no  longer  in  combination  with  other 
elements  and  therefore  then  have  no  existing  bonds ; 
hence  depositing  a  free  element  is  really  also  a  case 
of  change  of  valence  (see  Appendix  I). 

In  subtracting  one  valence  from  another  the  differ- 
ence may  have  the  negative  sign,  as  in  subtracting  3 
from  2 ;  the  sign  of  this  difference  need  not  be  con- 
sidered as  it  signifies  merely  the  direction  of  the 
current  but  not  the  amount;  hence  all  the  valences 
in  the  table  apply  equally  well  to  the  negative  as  to 
the  positive  values.  These  features  of  valences  are 
described  more  fully  in  Appendix  I. 

Example  5.  Depolarizer.  Change  of  valence.  How 
much  peroxide  of  manganese  is  required  as  a  de- 
polarizer in  a  dry  cell  for  a  discharge  of  100  ampere- 
hours?  In  this  reaction  2  MnO2  is  reduced  to  Mn2O3, 
the  remaining  atom  of  oxygen  being  that  which  per- 
forms the  operation  of  depolarizing  by  combining  with 
the  ion  which  would  otherwise  tend  to  be  set  free 
there  and  cause  polarization. 

The  valence  of  the  manganese  in  the  original  ma- 
terial is  4  (as  oxygen  here  has  a  valence  of  2) ,  while 
in  the  resulting  product  it  is  3  (the  oxygen  now  having 
6  bonds,  each  of  the  two  manganese  atoms  must 
have  3),  hence  the  difference  or  change  of  valence  is 
1.  From  the  table,  column  9  for  manganese,  valence 
1,  4.518  pounds  of  the  element  manganese  are  re- 
quired for  1000  ampere-hours,  hence  0.4518  Ib.  for 
100  ampere-hours.  This  is  for  the  element  man- 
ganese ;  the  corresponding  amount  of  the  peroxide  is 


38  ELECTROCHEMICAL  EQUIVALENTS 

then  determined  as  usual  by  the  well  known  chemical 
calculations ;  thus  the  molecular  weight  (or  more 
correctly  the  formula  weight)  of  the  peroxide  MnO2 
is  54.93  +  (16  x  2)  =  86.93,  and  that  of  manganese 
alone  is  54.93 ;  hence  0.4518  Ib.  of  Mn  x  86.93  ^ 
54.93  =  .715  or  about  3/4  Ib.  of  the  peroxide. 

The  same  result  may  be  obtained  without  involving 
the  change  of  valences,  but  it  will  be  found  to  be  far 
more  cumbersome.  In  that  case  write  out  the  com- 
plete chemical  equation  of  the  reaction  involving  the 
zinc,  the  manganese  oxides,  and  the  ammonium 
chloride.  Then  calculate  the  amount  of  zinc  con- 
sumed by  the  100  ampere-hours,  as  described  above, 
using  the  constants  in  the  table,  and  then  from  the 
equation  by  purely  chemical  calculations,  determine 
the  amount  of  the  peroxide  corresponding  to  that 
amount  of  zinc. 

Subscripts  may  be  ignored.  After  having  determined 
the  valence  involved  in  a  reaction,  the  subscripts  in 
the  chemical  formulas  of  compounds  can  be  ignored 
entirely  in  these  electrochemical  calculations.  For  a 
given  valence  of  an  element  an  ampere-hour  corre- 
sponds to  a  fixed  and  definite  amount  of  the  element 
and  is  entirely  independent  of  any  arbitrary  chemical 
formula. 

Thus  from  cuprous  chloride  CuCl  the  amount  of 
chlorine  involved  by  one  ampere-hour  is  exactly  the 
same  as  in  cupric  chloride  CuCl2,  namely  1.323  grams, 
altho  the  subscript  is  twice  as  great  in  the  second 
case ;  the  valence  of  the  chlorine  is  the  same  in 
both,  namely  1.  For  the  copper  the  subscripts  are 
the  same  in  both  (unity),  yet  the  amount  of  copper 
deposited  per  ampere  from  CuCl  is  twice  as  great  as 
from  CuCl2  because  the  valence  is  half  as  great. 
The  subscripts  are  important  for  determining  the 


EXAMPLES  39 

valences,  but  beyond  that  they  should  be  ignored  in 
such  calculations,  as  they  may  cause  confusion.  For 
the  indirect  method  of  calculation  in  which  the  whole 
chemical  equation  must  be  written  out,  the  subscripts 
are  of  course  important  for  balancing  the  equation 
and  must  be  considered  in  the  purely  chemical  part 
of  the  calculation. 

Coefficients  may  be  ignored.  What  was  said  above 
about  subscripts  is  equally  applicable  to  the  coeffi- 
cients in  chemical  formulas;  they  moreover  are  not 
even  necessary  to  determine  the  valence.  This  is 
illustrated  by  the  following  example. 

Example  6.  Ignoring  .coefficients.  How  much  nitric 
acid  will  be  required  in  a  Bunsen  cell  for  100  ampere- 
hours,  assuming  that  the  nitric  acid  HNO3  is  all 
reduced  to  nitric  oxide  NO? 

The  chemical  formula  for  this  reaction  is 

3  Zn  +  3  H2SO4.+  2  HNO3  =  3  ZnSO4  +  2  NO 
+  4H2O 

which  it  will  be  seen  contains  numerous  coefficients. 
In  the  simplest  and  most  direct  form  of  calculation 
based  on  the  change  of  valence,  all  that  is  necessary 
to  know  is  that  the  valence  of  the  nitrogen  in  the 
nitric  acid  is  5  and  in  the  nitric  oxide  it  is  2,  hence  the 
change  of  valence  is  3 ;  all  these  coefficients  may 
therefore  be  neglected,  and  in  fact  need  not  even  be 
known.  From  the  table  the  constant  for  nitrogen 
for  a  change  of  valence  of  3  is  0.3841  pounds  per  1000 
ampere-hours;  for  100  ampere-hours  it  is  therefore 
0.0384  Ib.  From  this  the  amount  of  the  acid  is  cal- 
culated by  the  usual  chemical  method;  thus  the 
atomic  weight  of  N  =  14.01,  and  the  molecular  weight 
of  HNO3  =  1.008  +  14.01  +  48.  =  63.02  ;  therefore 
0.0384  Ib.  x  63.02  -  14.01  =  .173  Ib.  of  nitric  acid ; 


40  ELECTROCHEMICAL  EQUIVALENTS 

this  of  course  refers  only  to  the  nitric  acid  itself  and 
does  not  include  the  water  in  which  the  commercial 
acid  is  dissolved. 

If  however  the  calculation  is  made  in  the  longer 
indirect  way,  that  is,  by  first  determining  electro- 
chemically  the  amount  of  zinc  corresponding  to  the 
100  ampere-hours,  and  then  chemically  the  amount  of 
nitric  acid  corresponding  to  this  amount  of  zinc, - 
the  coefficients  of  course  enter  into  the  calculation, 
tho  only  in  the  purely  chemical  part  of  it.  Thus  from 
the  table  100  ampere-hours  corresponds  to  .269  Ib.  of 
zinc,  no  matter  what  the  coefficient  of  the  zinc  is  in 
this  formula.  From  the  equation  3  Zn  corresponds  to 
2  HNO3,  hence  the  amounts  of  zinc  and  nitric  acid 
are  in  the  proportion  of  the  weights  of  these  two 
quantities.  The  atomic  weight  of  zinc  is  65.37  and 
the  molecular  weight  (or  formula  weight)  of  nitric 
acid  is  63.02  (see  above) ;  hence  .269  Ib.  x  (2  x  63.2) 
•*-  (3  x  65.37)  =  .173  Ib.  of  nitric  acid,  as  before. 

Intermediate  reactions  may  be  ignored.  The  reaction 
in  example  6  involves  an  intermediate  reaction  also; 
the  zinc  is  dissolved  in  the  sulfuric  acid  in  which  it 
replaces  the  hydrogen,  and  this  hydrogen  then  reduces 
the  nitric  acid ;  this  at  least  may  serve  as  a  simple 
explanation  of  the  reaction.  In  the  direct  method 
of  calculation  based  on  the  change  of  valence  all 
such  intermediate  reactions  may  be  ignored,  while 
in  the' chemical  part  of  the  indirect  method  they  may 
sometimes  have  to  be  known  hi  order  to  write 
out  the  chemical  equation.  The  amount  of  nitrogen 
oxidized  or  reduced  by  one  ampere-hour,  involving 
a  given  change  of  its  valence,  is  a  fixed  and  definite 
quantity,  and  is  entirely  independent  of  any  other 
reactions  which  may  be  occurring  at  the  same  time, 
except  of  course  if  they  are  resultant  reactions  of 


EXAMPLES  41 

a  purely  chemical  kind,  often  termed  secondary  re- 
actions. 

Invoked  reactions.  The  above  examples  illustrate 
the  simplest  kinds  of  cases  involving  calculations  of 
electrochemical  equivalents.  The  following  examples 
will  serve  to  illustrate  some  of  the  less  simple  cases 
which  involve  features  that  are  different  from  those  in 
the  more  usual  ones  and  which  might  sometimes  give 
rise  to  confusion. 

Example  7.  Nothing  set  free  or  dissolved  at  one  of  the 
electrodes.  If  the  cathode  is  in  copper  sulfate  and 
the  platinum  anode  is  in  ferrous  sulfate,  copper  will 
be  deposited  on  the  cathode  as  usual;  but  at  the 
platinum  anode  the  corresponding  SO4  ion  will  not 
set  free  oxygen  as  is  more  usual,  but  will  oxidize  the 
ferrous  sulfate  into  the  ferric,  hence  nothing  will  be 
set  free  or  dissolved  there.  The  iron  solution  acts  as 
a  depolarizer  at  the  anode  by  combining  with  the 
SO  4,  thereby  preventing  it  from  forming  a  film  of 
oxygen  gas  over  the  anode. 

However  the  somewhat  unusual  fact  that  nothing 
is  set  free  or  dissolved  at  the  anode  involves  no 
difficulties  in  the  electrochemical  calculation  for  that 
electrode  when  based  on  the  change  of  valence,  and 
need  lead  to  no  confusion.  The  iron  salt  has  been 
changed  at  that  electrode  from  ferrous  to  ferric, 
which  is  a  true  electrochemical  reaction ;  it  means 
that  its  valence  has  been  changed  from  2  to  3,  hence 
by  1  unit ;  the  amount  of  iron  so  changed  per  ampere- 
hour  is  therefore  found  directly  from  the  table, 
column  7,  for  valence  1,  namely  2.083  grams  per 
ampere-hour.  The  amounts  of  the  sulfates  cor- 
responding to  this  amount  of  the  iron,  are  then 
readily  determined  from  the  purely  chemical  calcula- 
tions. 


42  ELECTROCHEMICAL  EQUIVALENTS 

The  equation  of  this  reaction  is 

CuSO4  +  2  FeSO4  =  Cu  +  Fe2  (SO4)3 

The  valence  of  the  radical  SO4  is  2,  as  it  combines 
with  2  hydrogen  atoms  in  H2SO4;  from  its  valence 
the  valences  of  the  iron  in  these  ferrous  and  ferric 
salts  are  evident  from  their  formulas,  2  in  the  first 
and  (3  x  2)  -T-  2  =  3  in  the  second. 

The  amount  of  iron  salts  could  be  determined  also 
without  considering  the  valences  by  finding  first  how 
much  copper  will  be  deposited  by  a  given  current  and 
then  by  a  purely  chemical  calculation,  using  the 
above  equation,  determine  the  corresponding  amounts 
of  the  iron  salts. 

Example  8.  Nothing  set  free  or  dissolved  at  either 
electrode.  If  a  platinum  cathode  is  in  a  solution  of 
ferric  sulfate,  and  a  platinum  anode  is  in  a  solution 
of  ferrous  sulfate  (the  latter  like  in  example  7),  then 
at  the  cathode  the  ferric  sulfate  will  be  reduced  to 
the  ferrous,  while  at  the  anode  the  ferrous  will  be 
oxidized  or  adduced  to  the  ferric ;  hence  nothing  will 
be  set  free  or  dissolved  at  either  electrode.  The 
SO4  ions  will  go  from  the  cathode  to  the  anode. 

The  reaction  is 

Fe2(SO4)3  (at  cathode)  +  2  FeSO4  (at  anode)  = 
2  FeSO4  (at  cathode)  +  Fe2(SO4)3  (at  anode). 

The  valence  of  the  iron  in  the  ferric  state  is  3  and 
'in  the  ferrous  2,  hence  there  is  a  change  of  1,  and 
this  change  is  the  same  hi  amount  at  each  electrode, 
tho  of  opposite  sign,  which  merely  signifies  the  rela- 
tively reverse  direction  of  the  current.  The  electro- 
chemical equivalent  is  therefore  found  directly  from 
the  table  to  be  2.083  grams  of  iron  per  ampere-hour ; 
this  applies  to  either  electrode. 


EXAMPLES  43 

This  is  a  case  in  which  the  method  of  calculation 
based  on  the  change  of  valence  is  far  simpler  than 
with  the  older  methods,  as  there  is  now  nothing 
tangible  set  free  or  dissolved  at  either  electrode 
which  could  be  used  as  a  basis,  as  was  the  case  in 
all  of  the  other  examples.  The  iron  cannot  now  be 
used  as  a  basis  because  it  is  not  deposited  and  has  a 
different  valence  at  each  electrode ;  to  use  either  of 
these  valences  would  give  a  totally  wrong  result. 

A  possible  way  of  making  this  calculation  without 
considering  the  change  of  valence,  would  be  to  use 
the  radical  SO4  as  a  basis,  as  this  is  in  effect  trans- 
ferred from  one  electrode  to  the  other  just  as  the 
metal  is  hi  electroplating,  and  its  valence  is  the  same, 
namely  2,  in  both  of  the  salts,  hence  can  be  neg- 
lected ;  having  the  same  valence  its  electrochemical 
equivalent  at  each  electrode  is  the  same  per  ampere- 
hour. 

Its  electrochemical  equivalent  is  not  given  hi  the 
table  because  it  is  not  an  element,  but  it  can  readily 
be  determined  from  any  of  the  sulfates,  such  as 
FeSO4.  Thus  the  iron  in  this  sulfate  has  a  valence 
of  2,  hence  its  electrochemical  equivalent  from  the 
table  is  1.042  grams  per  ampere-hour.  As  every 
atom  of  iron  corresponds  to  one  molecule  of  SO4  the 
amount  of  the  latter  in  grams  per  ampere-hours  will 
be  in  the  proportion  of  then*  atomic  weights.  That  of 
iron  is  55.84  and  that  of  SO4  is  32.06  +  (16  x  4)  = 
96.06.  Hence  1.042  grams  x  96.06  •*-  55.84  =  1.79 
grams  of  SO4  per  ampere-hour. 

At  the  anode  one  SO4  combines  with  two  FeSO4  to 
form  one  Fe2(SO4)3;  hence  2  Fe  (atomic  weight 
2  x  55.84  =  111.68)  corresponds  to  one  of  SO4  (atomic 
weight  96.06).  As  there  are  1.79  grams  of  SO4  per 
ampere-hour,  there  will  be  1,79  x  111.68  -=-  96.1  = 


44  ELECTROCHEMICAL  EQUIVALENTS 

2.083  grams  of  iron  involved  at  each  electrode  per 
ampere-hour,  the  same  as  was  found  above  by  a  far 
simpler  calculation.  A  similar  calculation  made  for 
the  cathode  reaction  will  give  the  same  result  except 
that  what  is  a  gain  of  SO4  at  one  is  a  loss  at  the 
other. 

It  will  be  noticed  that  the  end  results  are  chemically 
the  same  as  those  at  the  start,  hence  nothing  has  been 
accomplished  other  than  changing  the  positions  of  the 
two  solutions,  which  should  be  separated  by  a  porous 
cup.  It  is  analogous  to  electroplating  in  which  the 
end  results  are  also  chemically  the  same,  the  metal 
being  merely  transferred  from  the  anode  to  the 
cathode. 

It  is  assumed  of  course  that  this  reaction  is  not 
carried  out  faster  than  the  solutions  in  contact  with 
the  electrodes  can  be  replaced  by  diffusion,  otherwise 
some  other  reactions  will  take  place,  like  the  deposi- 
tion of  iron  or  the  evolution  of  oxygen.  As  this 
reaction  involves  no  resultant  chemical  change  it 
should  require  no  more  voltage  than  that  necessary 
to  overcome  the  resistance ;  hence  using  a  voltage 
too  low  to  set  free  iron  or  oxygen,  ought  to  prevent 
these  other  reactions  from  taking  place. 

Example  9.  The  same  as  Example  8  but  involving  in 
addition  a  purely  chemical  reaction.  The  platinum 
anode  is  again  hi  a  solution  of  ferrous  sulfate,  but 
the  cathode  now  is  in  a  solution  of  chromic  and 
sulfuric  acid.  Again  nothing  will  be  set  free  or 
dissolved  at  either  electrode.  The  complete  equation 

is 

2  H2CrO4  +  6  H2SO4  +  6  FeSO4  = 

Cr2(S04)3  +  8  H20  +  3  Fe2(SO4)3 

The  chromic  acid  will  be  reduced  at  the  cathode 
which  would  form  a  precipitate  but  this  is  dissolved 


EXAMPLES  45 

in  the  sulfuric  acid  forming  chromium  sulfate. 
The  chromium  at  the  cathode  has  changed  its  valence 
from  6  to  3,  hence  the  difference  is  3  ;  its  amount  can 
therefore  be  found  directly  from  the  table.  At  the 
anode  the  change  of  valence  of  the  iron  is  1,  namely 
from  2  in  the  ferrous  to  3  in  the  ferric  state ;  hence 
its  amount  can  also  be  found  directly  from  the  table. 

The  sulfuric  acid  however  has  a  double  function, 
half  of  it  being  electrolyzed  to  give  the  SO4  to  the 
ferrous  sulfate  at  the  anode,  the  hydrogen  from  it 
going  to  fdrm  water,  while  the  other  half  acts  purely 
chemically  to  dissolve  the  reduced  chromic  acid, 
forming  chromium  sulfate  and  water.  The  latter 
half  must  therefore  not  be  included  in  the  electro- 
chemical calculations,  but  must  be  added  to  that 
required  electrochemically  in  order  to  get  the  total 
acid  for  the  complete  reaction.  In  such  complicated 
reactions  it  is  safest  to  use  the  chromium  or  the  iron 
in  the  electrochemical  calculations  and  then  calculate 
the  amount  of  sulfuric  acid  by  purely  chemical 
means  from  the  above  equation. 

The  metals  in  solution  at  the  anode  and  cathode 
being  different  (iron  and  chromium),  the  calculations 
might  again  be  made  as  suggested  in  the  previous 
example  8,  by  using  SO4  as  a  basis,  as  it  is  this  that 
may  be  said  to  be  what  is  transferred  from  one 
electrode  to  the  other. 

It  may  be  of  interest  to  note  here  that  this  reaction 
forms  an  odd  kind  of  storage  battery,  in  which  only 
the  two  liquids  enter  into  the  reaction  and  carry  the 
energy,  the  plates  themselves  remaining  completely 
unchanged.  The  fresh  liquids  could  be  supplied  to 
the  battery  as  the  source  of  the  energy,  and  the  ex- 
hausted liquids  only  (and  not  the  whole  battery) 
would  be  taken  to  a  power  station  and  recharged  by 


46  ELECTROCHEMICAL  EQUIVALENTS 

means  of  a  current.  One  of  the  objections  to  it  is 
that  it  is  a  two  fluid  battery,  hence  requires  porous 
partitions  to  keep  the  liquids  separated,  and  that  they 
will  nevertheless  gradually  contaminate  each  other. 

Example  10.  Nothing  is  set  free  or  dissolved  at  one  of 
the  electrodes,  and  the  current  appears  to  do  double  duty 
on  the  same  electrolyte.  If  the  electrodes  are  both  plati- 
num and  there  is  only  a  single  solution  of  cuprous 
chloride,  CuCl,  copper  will  be  deposited  at  the 
cathode  with  a  valence  of  1,  while  at  the  anode 
the  chlorine  will  raise  (oxidize,  or  better,  adduce) 
the  cuprous  to  cupric  chloride,  CuCl2,  hence  nothing 
will  be  set  free  or  dissolved  at  the  anode.  The 
chemical  equation  is 

2  CuCl  =  Cu  +  CuCl2 

The  amount  of  copper  deposited  per  ampere-hour 
is  readily  calculated  from  the  table,  remembering  that 
the  valence  now  is  1  and  not  2  as  is  more  usual; 
that  is,  there  will  be  twice  as  much  deposited  per 
ampere-hour  as  from  the  more  usual  copper  solutions. 
But  the  facts  that  nothing  is  set  free  or  dissolved  at 
the  anode  and  that  the  amount  of  cuprous  chloride 
which  is  changed  to  cupric  is  double  that  correspond- 
ing to  the  copper  deposited,  may  give  rise  to  some 
confusion. 

The  chlorine  which  had  been  combined  with  the 
copper  which  is  deposited  on  the  cathode,  tends  to  be 
set  free  at  the  anode,  but  it  there  combines  with 
some  of  the  cuprous  chloride,  CuCl,  to  form  the  cupric, 
CuCl2.  The  fact  that  one  molecule  of  the  cuprous 
chloride  is  completely  decomposed  at  the  cathode, 
while  at  the  same  time  another  molecule  of  it  is 
raised  to  the  cupric  salt  at  the  anode  by  the  same 
current,  explains  why  twice  as  much  of  the  original 
Solution  is  changed  when  compared  with  that  which 


EXAMPLES  47 

corresponds  to  the  amount  of  deposited  copper.  The 
above  chemical  equation  also  shows  that  in  this 
reaction  one  part  of  metallic,  free  copper  corresponds 
to  two  parts  of  the  original  solution. 

To  have  calculated  the  amount  of  cuprous  salt 
which  has  been  acted  upon  per  ampere-hour,  from 
the  amount  of  chlorine  arriving  at  the  anode,  or 
from  the  amount  of  copper  deposited,  would  have  led 
to  entirely  wrong  results ;  it  is  necessary  in  such 
cases  to  consider  the  actions  at  both  electrodes,  and 
in  this  particular  case  the  current  does  a  double  duty, 
as  the  same  current  changes  two  molecules  of  the 
same  compound,  one  at  each  electrode.  Removing 
some  of  the  copper  (chemically)  from  cuprous  chloride 
or  adding  some  chlorine  to  it  (chemically)  both  pro- 
duce the  same  effect,  namely  changing  some  of  it  to 
the  cupric  chloride ;  hence  in  that  sense  it  might  be 
said  that  the  chemical  changes  of  the  solution  are  in 
this  case  alike  at  both  electrodes. 

Example  1 1.  Exhaustion  of  the  same  electrolyte  at  both 
electrodes.  How  many  ampere-hours  will  it  require 
to  extract  all  of  the  lead  from  a  solution  of  nitrate 
of  lead  Pb(NO3)2  containing  100  grams  of  lead, 
when  electrolyzed  between  two  platinum  electrodes? 
In  this  case  the  lead  will  be  deposited  from  the 
solution  at  both  electrodes,  it.  being  reduced  at  the 
cathode  where  it  be  will  deposited  as  metallic  lead, 
and  it  will  be  oxidized  or  adduced  at  the  anode 
where  it  will  be  deposited  as  peroxide  of  lead.  The 
residual  solution  will  be  nitric  acid,  and  it  is  here 
assumed  that  this  will  not  redissolve  the  lead  on  the 
cathode  by  local  action. 

The  equation  is 

2  Pb(N03)2  +  H20  =  Pb  +  4  HNO3  +  PbO2 


48  ELECTROCHEMICAL  EQUIVALENTS 

The  valence  of  the  lead  in  the  nitrate  is  2,  in  the 
peroxide  it  is  4,  and  hi  the  form  of  metallic  lead  it  is 
0.  Hence  the  change  of  valence  at  each  electrode 
is  2 ;  being  the  same  at  both,  the  amount  of  lead 
deposited  on  each  electrode  will  be  the  same,  hence 
50  grams.  From  the  table  1  gram  at  valence  2  will 
require  0.2587  ampere-hours,  hence  50  grams  at  each 
electrode  will  require  50  x  .2587  =  12.94  ampere- 
hours. 

Or  it  may  be  calculated  without  involving  the 
changes  of  valence  by  finding  the  lead  deposited  as 
such  at  the  cathode  and  then  by  purely  chemical 
calculations  finding  the  corresponding  amount  at  the 
anode ;  the  equation  shows  these  two  to  be  the  same. 

Example  12.  Change  of  valence  involving  different 
signs.  Negative  Valences.  How  much  sulfur  would 
be  involved  per  ampere-hour  hi  the  oxidation  or 
adduction  of  hydrogen  sulfide,  H2S,  into  sulfuric 
acid,  H2SO4,  if  it  were  done  electrolytically?  The 
equation  is 

H2S  +  4  H2O  =  4  H2  +  H2SO4 

In  all  the  previous  examples  illustrating  the  more 
usual  cases  involving  a  change  of  valence,  the  two 
valences  of  the  elements  had  the  same  sign  before 
and  after  the  electrolysis,  and  then*  signs  need  there- 
fore not  be  considered.  But  in  some  cases  like  the 
present,  the  sign  of  the  valence  changes  and  therefore 
becomes  very  important. 

In  every  compound  the  bonds  representing  the 
valences  must  always  add  up  to  zero.  Those  of 
hydrogen  are  always  +  and  those  of  oxygen  nearly 
always  — .  In  H2S  the  sulfur  must  therefore  have 
two  negative  bonds,  hence  a  valence  of  -  2  to  balance 
the  two  positive  bonds  of  the  H2.  But  in  H2SO4  the 
sulfur  has  6  positive  bonds  (the  oxygen  having  8 


EXAMPLES  49 

negative  ones,  two  of  which  combine  with  the  hydro- 
gen), hence  has  a  valence  of  +  6. 

The  change  of  valence  being  the  algebraic  difference 
is  therefore  in  this  reaction  equal  to  the  difference 
between  -  2  and  +  6  which  is  8  (the  sign  of  this 
difference  is  no  longer  of  importance  as  it  merely 
refers  to  the  direction  of  the  current).  In  the  table 
the  highest  valence  given  is  6 ;  the  figure  for  valence 
1  is  1.196  grams  per  ampere-hour,  hence  for  a  valence 
of  8  it  will  be  one-eighth  of  this,  namely  0.150  grams 
of  sulfur,  as  the  same  current  now  has  to  neutralize 
8  times  as  many  bonds  per  gram.  This  is  a  very  small 
amount  of  sulfur  for  that  amount  of  electricity, 
hence  this  reaction  would  take  much  current  or  a 
long  time.  This  example  is  described  as  a  simple 
hypothetical  case  to  show  how  to  make  the  calcula- 
tions when  there  is  a  change  of  sign  of  the  val- 
ence ;  as  the  sulfur  would  have  to  pass  thru  the 
state  of  zero  valence  which  means  that  it  is  then  in 
its  free  state,  some  free  sulfur  is  likely  to  form  in  the 
solution.  In  practice  it  is  simpler  to  burn  the  H2S 
in  the  air  to  a  low  oxide  and  then  oxidize  a  solution 
of  this  to  a  higher  oxide  by  electrolysis. 

This  calculation  could  be  made  also  without  con- 
sidering this  change  of  valence,  by  determining  from 
the  table  the  amount  of  hydrogen  liberated  per 
ampere-hour  (disregarding  the  coefficient  and  sub- 
script) and  then  by  a  purely  chemical  calculation  (hi 
which  the  coefficients  and  subscripts  must  be  con- 
sidered) find  the  corresponding  amount  of  sulfur 
from  the  above  equation.  Thus,  from  the  table, 
0.03761  gram  of  hydrogen  is  liberated  per  ampere- 
hour.  From  the  second  half  of  the  equation,  for 
every  8  atoms  of  hydrogen  liberated  there  will  be  one 
of  sulfur;  from  their  atomic  weights  the  respective 


50  ELECTROCHEMICAL  EQUIVALENTS 

weights  will  therefore  be  as  8  x  1.008  is  to  32.06. 
Hence  0.03761  gram  of  hydrogen  per  ampere-hour  in 
this  case  corresponds  to  0.03761  x  32.06  -f-  8.064  = 
0.150  grams  of  sulfur  per  ampere-hour,  the  same  as 
before. 

Example  13.  A  similar  case.  When  nitric  acid  is 
reduced  to  ammonia  there  is  a  similar  change  of  sign 
of  the  valence,  but  hi  this  case  it  is  a  change  from 
+  to  —  as  it  is  a  reduction,  while  in  the  previous 
case  it  was  a  change  from  --  to  +,  as  it  was  an 
adduction  or  a  so-called  oxidation.  The  valence  of  the 
nitrogen  in  the  acid  HNO3  is  +  5  (+1  +  5-6  =  0), 
and  in  the  ammonia  NH3  it  is  —  3  (-3+3  =  0), 
hence  the  change  is  then*  algebraic  difference,  8. 

The  calculation  may  be  made  without  involving 
these  valences  by  starting  with  the  amount  of  oxygen 
which  would  have  to  be  set  free,  and  then  determin- 
ing the  nitric  acid  involved  by  a  purely  chemical 
calculation.  In  these  indirect  calculations  the  element 
which  is  set  free,  as  distinguished  from  merely  being 
changed,  is  always  a  good  basis  for  starting  such 
calculations,  as  was  also  shown  in  other  Examples. 

Example  14.  Partial  change  of  valence.  How  much 
nitric  acid  is  required  per  ampere-hour  when  used  as 
a  depolarizer  in  a  Bunsen  cell,  assuming  the  nitric 
acid  to  be  changed  into  ammonium  nitrate?  The 
equation  is 

4  Zn  +  4  H2SO4  +  2  HNO3  = 
4  ZnSO4  +  NH4NO3  +  3  H2O 

In  the  nitric  acid  the  valence  of  the  nitrogen  is 
+  5(  +  l  +  5-6  =  0),  and  in  the  first  part  (NH4)  of 
the  ammonium  nitrate,  it  is  -  3  (-  3  +  4  +  5  -  6  =  0), 
hence  the  change  of  valence  is  8.  But  part  of  the 
nitrogen  of  the  original  nitric  acid  does  not  change 
its  valence,  remaining  as  NO3 ;  this  part  is  therefore 


EXAMPLES  51 

not  involved  in  the  electrochemical  part  of  the  reac- 
tion. The  original  acid  does  a  double  duty;  the 
equation  shows  that  half  of  the  nitrogen  is  electro- 
chemically  converted  into  ammonia  and  the  other  half 
remains  as  NO3.  The  former  is  calculated  electro- 
chemically  for  a  change  of  valence  of  8,  which  is  then 
doubled  to  get  the  total. 

This  may  also  be  calculated  by  the  indirect  method 
without  involving  these  changes  of  valence.  The  zinc 
may  then  be  used  as  the  basis  for  the  electrochemical 
part  of  the  calculation,  the  corresponding  nitric  acid 
being  then  determined  from  it  by  a  purely  chemical 
calculation.  In  such  rare  and  involved  cases  as  this 
one  the  indirect  method,  tho  longer,  will  no  doubt  be 
the  safest  one  to  use  by  those  not  accustomed  to  the 
more  convenient  conception  of  changes  of  valences 
and  negative  valences. 


PART    II 


Section  V 

ELECTROLYSIS 

Theory  of  Electrolytic  Dissociation,  Faraday's  Law, 
Coulometers 

Introductory.  Conductors  of  electricity  may  be 
divided  into  two  classes  as  follows:  (1)  conductors 
of  the  first  class  which  experience  a  rise  of  tempera- 
ture due  to  the  passage  of  the  electric  current  but  do 
not  undergo  any  chemical  change  and,  (2)  conductors 
of  the  second  class,  in  which  the  passage  of  the 
electric  current  is  invariably  accompanied  by  chemical 
decomposition.  To  the  first  class  belong  the  metals 
and  their  alloys  and  a  few  non-metallic  elements 
such  as  carbon.  To  the  conductors  of  the  second 
class,  termed  electrolytes,  belong  solutions  of  acids 
bases,  and  salts,  either  fused  or  in  solution.  Elec- 
trolytes are  always  necessarily  compounds  and  never 
simple  elements.  Mercury,  for  example,  is  a  liquid 
conductor  but  it  is  not  electrolyzable.  While  under 
ordinary  conditions  pure  water  is  a  non-conductor,  it 
is  interesting  to  note  that  it  becomes  a  good  con- 
ductor of  electricity  when  an  acid,  a  base,  or  a  salt  is 
dissolved  in  it.  Although  salts  are  non-conductors  at 
ordinary  temperatures,  they  conduct  readily,  with 
simultaneous  decomposition,  when  heated  above  their 
melting  points.  Fused  salts  form  practically  the  only 
exception  to  the  rule  that  pure  chemical  compounds 

53 


54  ELECTROCHEMICAL  EQUIVALENTS 

are  non-conductors  of  electricity.  Practically  all 
organic  compounds,  with  the  exception  of  organic 
acids,  bases,  and  salts,  when  dissolved  in  water  are 
non-conductors.  Such  non-conducting  substances, 
among  which  alcohol,  ether,  starch,  and  sugar  may 
be  mentioned  as  typical  examples,  are  called  non- 
electrolytes.  It  should  be  borne  in  mind  that  the 
property  of  electrical  conductance  is  not  confined  to 
aqueous  solutions  alone.  The  decomposition  of  an 
electrolyte  resulting  from  the  passage  of  an  electric 
current  thru  its  solution  is  known  as  electrolysis. 

To  Faraday  we  owe,  not  only  our  knowledge  of  the 
fundamental  law  of  electrolysis,  but  also  the  precise 
definition  of  certain  terms  used  in  connection  with 
electrolytic  phenomena.  In  his  "Experimental  Re- 
searches"1 we  find  the  following  definitions:  "In 
place  of  the  term  pole,  I  propose  using  that  of  electrode, 
and  I  mean  thereby  that  substance,  or  rather  surface, 
whether  of  air,  water,  metal,  or  any  other  body,  which 
bounds  the  extent  of  the  decomposing  matter  in  the  di- 
rection of  the  electric  current.  The  surfaces  at  which, 
according  to  common  phraseology,  the  electric  current 
enters  and  leaves  a  decomposing  body,  are  most  impor- 
tant places  of  action,  and  require  to  be  distinguished 
apart  from  the  poles,  with  which  they  are  mostly, 
and  the  electrodes,  with  which  they  are  always,  in 
contact. 

.  .  .  The  anode  is  therefore  that  surface  at  which 
the  electric  current  .  .  .  enters :  ...  it  is  where 
oxygen,  chlorine,  acids,  etc.,  are  evolved.  .  .  .  The 
cathode  is  that  surface  at  which  the  current  leaves  the 
decomposing  body,  ...  the  combustible  bodies, 

1  "Experimental  Researches  in  Electricity,"  by  Michael 
Faraday.  Everyman's  Library,  Vol.  576,  pp.  112-114. 


ELECTROLYSIS 


55 


metals,  alkalies,  and  bases  are  evolved  there.  .  .  . 
Finally  I  require  a  term  to  express  those  bodies  which 
can  pass  to  the  electrodes,  or,  as  they  are  usually 
called,  the  poles.  ...  I  propose  to  distinguish  such 
bodies  by  calling  those  anions  which  go  to  the  anode 
of  the  decomposing  body;  and  those  passing  to  the 
cathode,  cations;  and  when  I  have  occasion  to  speak 
of  these  together,  I  shall  call  them  ions.  Thus,  the 
chloride  of  lead  is  an  electrolyte,  and  when  electrolysed 
evolves  the  two  ions  chlorine  and  lead,  the  former 
being  an  an  ion,  and  the  latter  a  cation." 

The  different  parts  of  an  electrolytic  cell  are  shown 
in  the  accompanying  diagram,  (Fig.  1).  It  is  impor- 
tant to  note  that,  contrary  to  common  usage,  it  is  the 
surfaces  of  the  plates  rather  _  „  _  „ 

than  the  plates  themselves, 
which  constitute  the  elec- 
trodes of  the  cell.  In  bat- 
teries the  cathode  is  gen- 
erally called  the  positive 
pole  because  the  current 

enters  the  outside   circuit 

,  .  . 
from  this  pole  ;    and   the 


lr  °f  ™ 

electrolytic  cell  showing  parts. 


anode  (usually  zinc)  is  then  called  the  negative  pole. 
This  is  reversed  in  electrolytic  baths.  Hence  the 
terms  positive  and  negative  poles  are  ambiguous, 
while  the  terms  anode  and  cathode  are  not.  The 
cations  move  with  the  current  through  the  electrolytic 
cell  toward  the  cathode  or  negative  plate  and  are 
positively  charged,  while  the  anions  migrate  in  the 
reverse  direction  toward  the  anode  or  positive  plate 
and  are  negatively  charged.  In  practice  it  is  a  matter 
of  great  importance  to  recognize  that  electrolytic 
changes  occur  only  in  the  molecular  layer  next  to  the 
electrodes.  Thus,  hi  the  electrolysis  of  a  solution  of 


56  ELECTROCHEMICAL  EQUIVALENTS 

copper  sulfate,  when  the  thin  layer  of  solution  next 
the  cathode  is  exhausted  of  copper,  hydrogen  will  be 
evolved,  unless  the  solution  is  vigorously  stirred  or 
the  cathode  is  rotated. 

Electrolytic  Phenomena.  The  products  obtained  at 
the  two  electrodes  of  an  electrolytic  cell  are  always 
different  and  may  be  collected  in  various  ways  de- 
pending upon  theur  nature.  When  gases  are  formed 
they  may  be  collected  in  appropriate  tubes.  When 
insoluble  solids  are  formed  they  generally  adhere  to 
the  electrode  surface  or  fall  to  the  bottom  of  the  cell 
as  a  precipitate.  When  soluble  substances  are 
produced  it  is  customary  to  surround  one  of  the 
electrodes  with  a  porous  cup,  or  to  interpose  some 
sort  of  porous  diaphragm  between  the  electrodes, 
which  will  minimize  the  diffusion  of  the  product  of 
electrolysis  from  the  vicinity  of  the  electrode  at 
which  it  is  formed.  When  a  current  of  electricity  is 
passed  between  two  platinum  plates  immersed  in  a 
solution  of  silver  nitrate,  metallic  silver  is  deposited 
at  the  cathode  while  oxygen  together  with  nitric  acid 
is  set  free  at  the  anode.  The  two  ions,  Ag  and  NO'3, 
are  discharged  at  the  cathode  and  anode  respectively : 
the  NO3  radical  is  then  assumed  to  react  with  the 
water  to  produce  nitric  acid  and  oxygen  as  indicated 
by  the  equation 

2  NO3  +  H20  =  2  HNO3  +  O 

The  interaction  of  the  NO3  ion  and  the  water  hi 
which  the  electrolyte  was  dissolved  is  known  as 
secondary  action.1 

1  While  the  above  explanation  of  secondary  action  is  not  in 
accord  with  the  generally  accepted  theory  of  LeBlanc,  Zeit. 
Phys.  Chem.  11,  805  (1893),  based  on  the  primary  decomposi- 
tion of  water,  for  all  practical  purposes  it  may  be  assumed  to  be 
correct. 


ELECTROLYSIS  57 

When  a  current  of  electricity  is  passed  between 
platinum  plates  immersed  in  a  solution  of  potassium 
nitrate,  hydrogen  is  liberated  at  the  cathode  and 
oxygen  at  the  anode.  An  examination  of  the  solution 
in  the  neighborhood  of  the  electrodes  reveals  the 
presence  of  potassium  hydroxide  at  the  cathode  and 
nitric  acid  at  the  anode.  In  this  case  the  two  ions, 
K  and  NO  '3,  are  discharged  at  then-  respective  elec- 
trodes and  then  a  secondary  reaction  may  be  assumed 
to  take  place  between  each  discharged  ion  and  the 
water,  as  shown  by  the  following  equations 

K  +  H2O  =  KOH  +  H     (reaction  at  cathode1) 

2  NO3  +  H2O  =  2  HNO3  +  O     (reaction  at  anode1) 

If,  hi  this  experiment,  the  negative  terminal  of  plati- 
num is  replaced  by  a  cup  of  mercury,  a  portion  of  the 
potassium  will  be  dissolved,  forming  an  amalgam,  thus 
confirming  the  primary  separation  of  metallic  potas- 
sium at  the  cathode.  The  reactions  taking  place  at 
the  electrodes  during  electrolysis  are  opposite  in 
character ;  oxidation  invariably  occurs  at  the  anode  while 
reduction  invariably  occurs  at  the  cathode.  These  facts 
are  of  extreme  practical  importance  and  are  often 
either  overlooked  or  are  insufficiently  emphasized 
in  introductory  textbooks  of  electrochemistry.  The 
anode  and  cathode  reactions  accompanying  the  elec- 
trolysis of  potassium  nitrate,  as  given  above,  may  be 
cited  as  illustrations  of  this  generalization. 

Theory  of  Electrolytic  Dissociation.  When  an  elec- 
trolyte is  dissolved  in  water,  all  of  the  properties  of 
the  solution  indicate  that  a  larger  number  of  dissolved 
units  are  present  than  in  a  solution  of  a  non-elec- 

1  More  properly  these  equations  should  be  written  ionically, 
thus;  K  +  H.OH  =  K  +  OH'  +  H 

2NO3  +  H.OH  =  2H  + 


58  ELECTROCHEMICAL  EQUIVALENTS 

trolyte  of  the  same  concentration.  Since  electrolytes 
are  believed  to  conduct  the  electric  current  by  virtue 
of  particles,  called  ions,  formed  from  the  molecules  of 
the  electrolyte,  it  is  assumed  that  these  ions  together 
with  the  undissociated  molecules  are  responsible  for 
the  abnormal  behavior  of  electrolytic  solutions.  This 
hypothesis,  put  forward  by  Arrhenius  in  1887,  is  known 
as  the  theory  of  electrolytic  dissociation.  The  fundamental 
assumptions  involved  in  this  theory  are  as  follows : 

(a)  When  the  molecules  of  an  electrolyte  are  dis- 
solved in  water  some  of  them  undergo  dissociation 
into   ions.     Thus,   potassium   chloride    (KC1)     disso- 
ciates into  the  ions  K  and  Cl'. 

(b)  The  extent  to  which  the  molecules  dissociate  is 
dependent  upon  the  dilution  of  the  solution ;  the  more 
dilute   the    solution,    the    greater   is   the    degree    of 
dissociation. 

(c)  Each  ion  is  highly  charged  with  electricity.    It 
is  this  electrical  charge  which  differentiates  an  ion 
from   the    corresponding   atom,    the    usual   chemical 
properties  of  an  element  being  greatly  modified  by  the 
presence    of    an    electrical    charge.    Thus,    atomic 
potassium  reacts  violently  with  water  to  form  hy- 
drogen   and    potassium    hydroxide,    whereas    ionic 
potassium  is  wholly  without  action  on  water. 

(d)  The  ions  resulting  from  the  dissociation  of  an 
electrolyte  are  of  two  kinds.     One  kind  of  ion  carries 
a  positive  charge,  and  the  other  carries  a  negative 
charge.     Since  the  solution,  as  a  whole,  is  electrically 
neutral,  it  follows  that  the  sum  of  the  positive  and 
negative  charges  must  be  equal.    The  character  of 
the  charge  carried  by  an  ion  may  be  indicated  by 
writing  the  usual  plus  or  minus  signs  over  the  symbols 
of  the  ions  or  preferably  by  the  use  of  a  dot  (•)  for  a 
positive  charge  and  of  a  dash(')  for  a  negative  charge. 


ELECTROLYSIS  59 

Thus,  the  electrolytic  dissociation  of  potassium  chloride 
into  positively  charged  potassium  and  negatively 
charged  chlorine  ions  may  be  represented  by  the  equation 

KC1  =  K  +  Ci 

or  KC1  =  K  +  Cl' 

Molecules  which  undergo  dissociation  into  two  ions 
are  known  as  binary  electrolytes,  while  those  which 
yield  on  dissociation  three  or  four  ions  are  called 
ternary  or  quaternary  electrolytes  respectively.  The 
following  equations  are  examples  of  the  dissociation 
of  ternary  and  quaternary  electrolytes 

K2S04  =  2  K  +  S0"4, 

BaCl2  =  Ba  +  2  Cl', 

AlCla  =  Al  +  3  Cl'. 

(e)  The  properties  of  a  solution  of  an  electrolyte 
are  dependent  upon  both  the  ions  and  the  undisso- 
ciated  molecules.  The  ions  are  in  general  more 
active  chemically  than  the  molecules  from  which  they 
are  derived  and  consequently  the  influence  of  the 
ions  is  predominant  in  deterrnining  the  properties  of 
a  solution  of  an  electrolyte. 

The  theory  of  electrolytic  dissociation,  while  not 
free  from  defects,  has  proven  to  be  a  generalization  of 
great  value  in  the  development  of  the  science  of 
electrochemistry.  All  of  the  changes  which  occur 
during  electrolysis  can  be  satisfactorily  explained  by 
means  of  this  theory.1 

1  The  reader  who  desires  further  information  concerning  the 
theory  of  electrolytic  dissociation  is  referred  to  the  following 
books  where  a  clear  exposition  of  the  theory  together  with 
some  of  its  applications  will  be  found : 

"  Theory  of  Electrolytic  Dissociation  "  —  Jones  (Macmillan 
Co.) ;  "  The  Theory  of  Electrolytic  Dissociation  "  —  Talbot 
and  Blanchard  (Macmillan  Co.). 

"The  Nature  of  Solution  "—Jones  (D.Van  Nostrand  Co.). 


60 


ELECTROCHEMICAL  EQUIVALENTS 


Migration    of    the 
local   phenomenon 


~ 


Copper  Sulphate 
+ Agar Agar 


Ions.  That  electrolysis  is  not  a 
taking  place  in  the  immediate 
neighborhood  of  the  elec- 
trodes, but  involves  an 
actual  migration  of  the  ions 
of  the  electrolyte,  may  be 
shown  by  a  variety  of  ex- 
periments of  which  the  fol- 
lowing is  one  of  the  most 
striking.  The  lower  part 
of  the  U-tube  shown  in 
Fig.  2  is  charged  with  a 

Fig.  2.— Diagram  of  an  exper-  dilute  solution  of  copper 
0  U1UStrate  migration  sulfate  containing  about  5 
per  cent  of  agar  agar  and 
is  then  allowed  to  stand  until  the  solution  has  set  to 
a  jelly.  Dilute  solutions  of  copper  sulfate  may  be  shown 
to  be  completely  dissociated  into  ions  as  indicated  by 
the  equation 

CuSO4  =  Cu  +  SO"4 

Since  pure,  anhydrous  copper  sulfate  is  known  to 
be  colorless,  and  since  sodium  sulfate,  potassium 
sulfate,  and  sulfuric  acid,  all  of  which  substances 
contain  the  SO"4  ion,  are  colorless,  it  follows  that  the 
blue  color  of  a  dilute  solution  of  copper  sulfate  must 
be  ascribed  to  the  Cii  ion  alone.  This  conclusion  is 
confirmed  by  the  fact  that  dilute  solutions  of  all 
cupric  salts  have  the  same  color. 

When  the  solution  in  the  U-tube  has  solidified,  the 
position  of  the  surface  of  the  jelly  hi  each  arm  of  the 
U-tube  is  marked  by  means  of  strips  of  gummed 
paper  pasted  on  the  outside  of  the  tube.  Then  some 
colorless  electrolyte,  such  as  a  solution  of  potassium 
nitrate  to  which  agar  agar  has  been  added,  is  intro- 
duced into  each  arm  of  the  U-tube.  After  the  agar 


ELECTROLYSIS  61 

agar  has  set  to  a  jelly,  a  few  cubic  centimeters  of  the 
potassium  nitrate  solution  containing  no  agar  agar  is 
added  to  each  arm  of  the  tube  and  two  platinum 
plates  introduced  as  shown  in  the  diagram.  The 
tube  is  now  immersed  in  ice-water  to  prevent  the 
softening  of  the  jelly  by  the  heat  developed  by  the 
passage  of  the  electric  current.  On  applying  a  current 
of  110  volts  with  a  16  candle-power  lamp  included 
in  the  circuit,  the  blue  solution  which  owes  its  color 
to  the  presence  of  Cu  ions  will  be  seen  to  move 
toward  the  cathode,  ascending  on  the  left-hand  side 
and  descending  on  the  right-hand  side  of  the  U-tube. 
While  solutions  containing  SO"*  ions  are  colorless,  it 
is  reasonable  to  infer  that  these  ions  migrate  in  the 
opposite  direction.  In  fact  the  experiment  may  be  so 
modified  as  to  reveal  the  actual  movement  of  the 
SO  "4  ions  toward  the  anode.  The  agar  agar  which  is 
added  to  prevent  the  transference  of  water  with  the 
current,  has  been  shown  to  increase  the  resistance  of 
the  solution  relatively  little. 

By  slight  modifications  of  the  above  experiment,  the 
actual  speeds  of  the  ions  under  a  definite  potential 
gradient  have  been  accurately  determined.    The  ac- 
companying table  gives  the  speeds  of  some  of  the  more 
common  ions  in  centimeters  per  second  when  measured 
in  dilute  aqueous  solution  at  18°C.  under  a  potential 
difference  of  1  volt  between  plates  1  centimeter  apart. 
Cations     Speed,  cm./  sea.      An  ions      Speed,  cm./  sec. 
H  0.003294  OH'          0.001802 

Li  0.000346  Cl'  0.000677 

Na  0.000450  NO'3         0.000640 

K  0.000669  C1O'3        0.000570 

NH4         0.000667 
Ag  0.000559 

Cu  0.000444 


62  ELECTROCHEMICAL  EQUIVALENTS 

It  will  be  observed  that  the  two  fastest  moving  ions 
are  the  H  ion  and  the  OH'  ion,  the  former  having  a 
speed  nearly  twice  that  of  the  latter. 

It  has  been  shown  that  the  speeds  of  the  ions  are 
specific  properties,  being  uninfluenced  by  the  presence 
of  other  ions  hi  the  same  solution.  It  has  also  been 
shown  that  an  increase  in  the  difference  of  potential 
between  the  plates  of  an  electrolytic  cell  causes 
proportional  increase  in  the  speed  with  which  the 
ions  move.  Notwithstanding  the  fact  that  the  ions 
move  so  slowly  under  a  fall  of  potential  of  1  volt  per 
centimeter,  it  may  be  shown  that  enormous  forces  are 
involved  in  imparting  to  the  ions  speeds  of  the  order 
of  magnitude  of  those  given  in  the  above  table.  It 
has  been  calculated,  for  example,  that  a  force  equal 
to  a  weight  of  299,000,000  kilograms  is  necessary  to 
impart  to  the  H  ion  a  speed  of  0.003294  cm.  per  sec. 
at  18°C.  The  magnitude  of  this  force  is  to  be  as- 
cribed to  the  extremely  small  mass  and  the  relatively 
large  surface  of  the  H  ion. 

Faraday  s  Law.  The  quantitative  relation  between 
the  amount  of  electricity  passing  thru  a  solution  of 
an  electrolyte  and  the  resulting  chemical  action  was 
discovered  by  Faraday  about  1835.  In  his. experi- 
ments Faraday  varied  the  size  and  nature  of  the 
electrode  surfaces,  the  concentration  of  the  elec- 
trolyte, and  the  amount  of  current  passing  thru 
the  solutions  in  a  given  time.  In  all  cases  he  found 
that  the  same  current  produced  the  same  amount  of 
chemical  decomposition,  or  in  other  words,  for  the 
same  electrolyte  the  amount  of  chemical  decomposition  is 
directly  proportional  to  the  amount  of  electricity  which  is 
passed  thru  the  solution  of  the  electrolyte.  When  solu- 
tions of  different  electrolytes  were  subjected  to  the 
action  of  the  same  current  by  placing  them  in  series 


ELECTROLYSIS 


63 


in  the  circuit,  Faraday  found  that  the  masses  of  the  prod- 
ucts of  electrolysis  were  directly  proportional  to  their  chemi- 
cal equivalents.  By  the  term  "  chemical  equivalent "  is 
meant  the  ratio  of  the  formula-weight  of  a  substance 
to  its  valence.  Thus,  the  formula  weight  of  silver 
is  107.88  and  its  valence  is  1,  hence  its  chemical 
equivalent  is  107.88 ;  similarly,  the  formula-weight, 
of  the  SO  "4  ion  is  96.06  and  its  valence  is  2,  therefore 
its  chemical  equivalent  is  48.03. 

The  foregoing  statements  of  the  results  of  Faraday's 
experiments  may  be  combined  in  a  single  generaliza- 
tion as  follows  :  When  the  same  quantity  of  electricity  is 
passed  thru  one  or  more  solutions  of  the  same  or  different 
electrolytes,  the  masses  of  the  substances  which  separate  at  the 
electrodes  are  directly  proportional  to  their  chemical  equivalents, 
and  are  independent  of  the  concentration  and  temperature  of 
the  solutions,  the  extent  of  the  electrode  surfaces,  and  all  other 
circumstances.  This  generalization  is  known  as  Faraday's 
Law  and  may  be  regarded  as  the  fundamental  law  of 
electrochemical  science. 

The  meaning  of  the  law  may  be  illustrated  by  the 
following  experiment :  If  solutions  of  hydrochloric 


fMWH 


HCl          H2SO<         KCl         'CuSfk        AuCh        F*Clz 
Fig.  3. —  Diagram  of  an  experiment  illustrating  Faraday's  law. 

acid  (HCl),  sulfuric  acid  (H2SO4),  potassium  chloride 
(KCl),  cupric  sulfate  (CuSO4),  auric  chloride  (AuCls), 
ferrous  chloride  (FeCl2),  and  ferric  chloride  (FeCla) 
are  placed  in  different  cells,  as  shown  in  Fig.  3,  and 
are  then  subjected  to  the  action  of  the  same  quantity 


64  ELECTROCHEMICAL  EQUIVALENTS 

of  electricity  by  connecting  them  in  series  with  a 
battery  of  storage  cells,  it  will  be  found  that  when 
1.008  grams  of  hydrogen  is  liberated  from  each  of 
the  two  acids.  35.45  grams  of  chlorine  will  be  set  free 
from  each  of  the  chloride  solutions,  96.06/2  =  48.03 
grams  of  SO4  will  be  set  free  from  the  sulfuric  acid 
and  cupric  sulfate,  while  the  amounts  of  the  metals 
deposited  at  the  cathode  surfaces  of  the  respective 
cells  will  be  39.10  grams  of  potassium,  63.57/2  =  31.7 
grams  of  copper,  197.2/3  =  65.7  grams  of  gold,  55.84/2 
=  27.92  grams  of  ferrous  iron,  and  55.84/3  =  18.61 
grams  of  ferric  iron. 

The  foregoing  experiment  illustrates  the  fact  that 
the  quantity  of  substance  set  free  by  a  given  quantity 
of  electricity  increases  inversely  as  its  valence  in  the 
solution  employed ;  thus,  27.92  grams  of  ferrous  iron 
is  liberated  by  the  same  current  which  deposits  18.61 
grams  of  ferric  iron.  This  point  is  of  importance  in 
connection  with  the  economic  use  of  electricity  in  all 
electrolytic  processes.  The  validity  of  Faraday's  law 
has  been  tested  by  numerous  experiments  carried 
out  with  the  utmost  care.  It  has  been  found  to  hold, 
not  only  for  all  solvents,  but  also  for  fused  elec- 
trolytes as  well. 

The  Electrochemical  Constant.  Since  the  same  quantity 
of  electricity  —  positive  or  negative  —  is  always 
carried  by  a  univalent  ion,  this  quantity  may  be 
considered  as  the  unit  of  ionic  charge.  A  bivalent 
ion  will  thus  carry  two  unit  charges  and  an  n-valent 
ion  will'  carry  n  unit  charges.  In  other  words,  we 
may  think  of  valence  as  representing  the  number  of 
unit  charges  of  electricity  which  are  associated  with 
the  respective  ions.  According  to  this  view  Faraday's 
law  may  be  stated  as  follows :  Chemically  equivalent 
masses  of  matter  possess  the  same  capacity  for  electricity. 


ELECTROLYSIS  65 

The  precise  measurement  of  this  fundamental  quantity 
of  electricity  is  obviously  a  matter  of  great  scientific 
and  practical  importance.  It  can  be  determined  by 
passing  a  known  quantity  of  electricity  thru  a  solu- 
tion of  an  electrolyte  and  weighing  the  metal  deposited 
at  the  cathode  surface  or  measuring  the  volume  of 
gas  set  free. 

The  most  satisfactory  results  have  been  obtained 
when  a  neutral  solution  of  silver  nitrate  is  used, 
containing  about  15  parts  of  the  salt  to  100  parts  of 
water,  and  with  a  current  density  of  about  0.01 
ampere  per  square  centimeter.  The  silver  is  de- 
posited on  a  platinum  dish  the  inner  surface  of  which 
serves  as  the  cathode,  while  a  silver  plate,  wrapped 
hi  filter  paper  to  retain  any  particles  of  silver  which 
may  be  detached  by  the  current,  constitutes  the 
anode  surface. 

The  unit  of  quantity  of  electricity  is  the  coulomb. 
This  may  be  defined  as  the  quantity  of  electricity 
which  has  passed  through  a  circuit  when  a  current  of 
1  ampere  has  been  flowing  constantly  for  1  second. 
The  mass  of  a  substance  in  grams  deposited  by  1 
coulomb  of  electricity  is  commonly  called  the  elec- 
trochemical equivalent,  of  the  substance. 

The  accepted  value  of  the  electrochemical  equiva- 
lent of  silver  is  0.00111800  gram  per  coulomb.  It  is 
evident,  therefore,  that  107.88  +  0.00111800  =  96493.7 
coulombs  of  electricity  will  be  required  to  deposit  the 
equivalent  weight  of  silver  in  grams. 

Since  electrochemical  equivalents  are  proportional 
to  chemical  equivalents  (Faraday's  law),  it  is  evident 
that  96493.7  coulombs  of  electricity  will  be  required  to  liberate 
the  equivalent  weight  of  any  ion.  This  number,  96493.7 
coulombs,  represents  the  fundamental  electrochemical 
unit,  and  is  called  the  electrochemical  constant  or  tbefaraday. 


66 


ELECTROCHEMICAL  EQUIVALENTS 


Coulomders.  (Voltameters.)  As  has  been  shown,  the 
quantity  of  electricity  passing  through  any  electric 
circuit  can  be  ascertained  by  determining  the  amount 
of  chemical  change  produced  at  an  electrode  surface. 
An  electrolytic  cell,  so  arranged  as  to  measure  the 
quantity  of  electricity  which  has  passed  through  it  by 
the  amount  of  chemical  action  it  produces,  is  called  a 
coulometer  or  a  voltameter,  the  former  term  being 
preferable.  There  are  three  general  types  of  coulom- 
eter in  use,  viz.,  (1)  weight  coulometers,  (2)  volume 
coulometers,  and  (3)  titration  coulometers.  These 
will  be  considered  very  briefly  in  the  subsequent 
paragraphs. 

Weight  Coulometers.  (a)  The  Silver  Coulometer.  In 
the  weight  coulometer,  as  the  name  implies,  the 
quantity  of  electricity  is  determined  by  measuring  the 
gain  in  weight  of  the  cathode  plate  due  to  the  deposi- 
tion of  metal  from  the 
electrolyte.  The  most 
accurate  of  all  coulom-' 
eters  is  the  silver 
coulometer.  This  in- 
strument has  already 
been  mentioned  in  con- 
nection with  the  deter- 
mination of  the  electro- 
chemical constant  (p. 
65).  The  silver  cou- 
lometer used  and  rec- 
ommended by  Richards 
Fig.  4. — Simple  silver  coulometer.  ,  TT  .  ,  ,  . 

and  Heimrod  1  is  shown 

in  Fig.  4.    It  consists  of  a  large  platinum  crucible  E,  the 

inner  surface  of  which  constitutes  the  cathode,  a  piece 

of  pure  silver  C,  which  forms  the  anode  surface,  a 

1  Zeit.  phys.  Chem.  41,  302.  (1902). 


ELECTROLYSIS  67 

porous  cup  D,  to  retain  any  particles  of  silver  which 
may  be  detached  mechanically  by  the  current,  and 
the  glass  insulating  supports  A  and  B.  The  electro- 
lyte consists  of  a  neutral  solution  of  silver  nitrate, 
prepared  by  dissolving  20  to  40  grams  of  pure  silver 
nitrate  in  100  grams  of  distilled  water.  By  weighing 
the  platinum  crucible  before  and  after  the  passage  of 
the  current,  the  amount  of  electricity  which  has 
flowed  through  the  coulometer  may  be  computed  from 
the  electrochemical  equivalent  of  silver,  0.00111800 
gram  per  coulomb.  The  mean  error  of  a  single  de- 
termination is  about  0.03  per  cent  for  a  deposit 
weighing  not  less  than  500  milligrams.  The  current 
density  must  not  exceed  0.2  ampere  per  square  centi- 
meter of  anode  surface  or  0.02  ampere  per  square 
centimeter  of  cathode  surface.  Care  should  be  taken 
to  insure  the  removal  of  the  last  traces  of  silver 
nitrate  solution  before  weighing  the  crucible.  This  is 
accomplished  by  washing  with  distilled  water  until 
the  washings  give  no  turbidity  with  a  solution  of  hy- 
drochloric acid.  The  crucible  is  then  dried  in  an  air 
bath  and  weighed.  The  solution  of  silver  nitrate 
may  be  used  repeatedly  until  a  deposit  corresponding 
to  3  grams  of  silver  per  100  cc.  of  solution  has  been 
reached. 

A  simple  and  inexpensive  form  of  silver  coulometer 
has  recently  been  designed  by  the  United  States 
Bureau  of  Standards  1  for  general  use.  The  following 
description  of  the  apparatus  is  taken  verbatim  from 
the  official  publication. 

"The  anode  was  made  in  the  form  of  a  large  ring 
set  in  a  glass  dish  containing  the  electrolyte.  This 
silver  ring  was  made  large  to  minimize  the  difficulties 

1  Bull.  Bureau  of  Standards.    Vol.  10.  p.  529. 


68 


ELECTROCHEMICAL  EQUIVALENTS 


with  the  anode  slime.  The  cathode  was  a  small 
platinum  ring  resting  in  a  shallow  glass  dish  sub- 
merged in  the  electrolyte  and  so  arranged  that  the 
whole  might  be  lifted  out  together.  As  this  platinum 

ring  weighed  only 
10.5  g.,  the  largest 
item  of  expense  was 
reduced  to  about  one- 
tenth  that  of  the  large 
size  standards." 
It  is  not  intended 
that  this  form  should 
be  used  in  any  work 
requiring  the  highest 
precision,  but  it  has 
been  shown  that  it 
may  be  relied  on 


of  1  per  cent.  The 
arrangement  of  the  parts  is  shown  hi  the  accompany- 
ing drawing  (Fig.  5). 

(b)  The  Copper  Coulometer.  In  this  instrument  the 
anode  surface  usually  consists  of  two  sheets  of  pure 
copper  with  a  thin  sheet  of  platinum  or  copper  be- 
tween them  serving  as  the  cathode  surface.  The 
electrolytic  solution  recommended  by  Oettel l  for  the 
copper  coulometer  has  the  following  composition : 

Crystallized  Cupric  Sulfate  15  grams 

Cone.  Sulfuric  Acid  (Sp.  Gr.  1.84)  5  grams 

Alcohol  95  per  cent  5  c.  c. 

Distilled  Water  100  c.  c. 

When  the  current  density  is  so  adjusted  that  it  does 

not  exceed  0.015  ampere  per  square  centimeter  of 

1  Chem.  Zeit.  77,  543  (1893). 


ELECTROLYSIS 


69 


cathode  surface,  it  is  claimed  by  Oettel  that  the 
copper  coulometer  will  give  results  which  agree 
perfectly  with  those  obtained  with  the  silver  coulom- 
eter. It  has  been  shown,  however,  that  there  are 
several  inherent  defects  in  the  copper  coulometer 
which  render  it  a  less  trustworthy  instrument  than 
the  silver  coulometer.  Thus,  the  copper  deposited 
at  the  cathode  surface  dissolves  slightly  in  acid 
cupric  sulfate  forming  a  cuprous  salt,  thereby 
diminishing  the  weight  of  the  cathode  plate.  If  a 
neutral  solution  of  cupric  sulfate  be  used,  there  is 
too  great  a  gain  in  the  weight  of  the  cathode  plate 
owing  to  the  deposition  of  cuprous  oxide  resulting 
from  the  hydrolysis  of  cuprous  sulfate.  As  the 
temperature  rises  the  proportion  of  cuprous  ions  to 
cupric  ions  increases,  causing  too  great  an  increase  in 
the  weight  of  the  deposit.  To  reduce  errors  due  to 
oxidation  it  is  often  recommended  that  a  slow  current 
of  carbon  dioxide 
be  bubbled  through 
the  solution.  The 
mean  error  of  a 
single  determina- 
tion with  the  cop- 
per coulometer  is 
about  0.2  per  cent. 
The  advantages  of 
the  copper  coulom- 
eter over  the  sil- 
ver coulometer  are 


Fig.  6. —  Copper  coulometer. 


that  it  is  cheap  and  that  the  copper  deposit  is  more 
adhesive  than  the  silver  deposit.  A  satisfactory  form 
of  copper  coulometer  is  shown  hi  Fig.  6. 

Volume    Coulometers.    The  best   known    coulometer 
of  this  type  is  the  so-called  water-coulometer.    In 


70 


ELECTROCHEMICAL  EQUIVALENTS 


this  instrument  the  total  volume  of  electrolytic  gases, 
or  the  volume  of  either  one  or  the  other  of  the  con- 
stituent gases  of  water,  is  measured.  The  form  of 

water-coulometer  devised 
by  F.  Kohlrausch 1  is 
shown  in  Fig.  7.  A  glass 
tube  graduated  into  1/10 
cc.  serves  to  measure  the 
volume  of  the  gases 
evolved  by  the  passage  of 
the  current  thru  water 
which  has  been  made 
conducting  by  the  addi- 
tion of  sulfuric  acid. 
The  graduated  tube  is 
fitted  into  a  shallow  glass 
reservoir  of  about  500 

Fig.  7.— Volume  ™^ometero7cc-  capacity  by  means  of 
Kohlrausch.  a     ground     joint.      Thru 

two  tubulures,  fitted  with 

rubber  stoppers,  electrical  connection  is  established 
with  two  platinum  plates.  A  small  thermometer  is 
sealed  into  the  upper  part  of  the  graduated  tube  to 
enable  the  experimenter  to  determine  the  temperature 
of  the  gas.  Kohlrausch  recommends  that  a  solution 
of  sulfuric  acid,  sp.  gr.  1.14,  be  used  to  fill  the  tube 
and  the  reservoir.  When  the  electric  current  to  be 
measured  is  passed  thru  the  solution,  the  uncor- 
rected  volume  of  the  resulting  mixture  of  hydrogen 
and  oxygen  is  read  directly  on  the  graduated  tube. 
By  means  of  suitable  tables  the  reduction  of  the 
volume  of  the  gas  to  standard  conditions  may  be 
readily  performed,  and,  knowing  that  1  coulomb  of 
electricity  liberates  0.17403  cc.  of  hydrogen  and  oxygen 
1  Elektrotech.  Zeit.  6,  190.  (1885). 


ELECTROLYSIS 


71 


in  molecular  proportions  at  0°  and  760  mm.  pressure, 
the  quantity  of  electricity  whicji  has  passed  thru 
the  circuit  can  be  easily  computed.  The  convenience 
in  reading  the  volume  of  gas  corresponding  to  the 
current  which  passes  thru  the  coulometer  is  offset 
by  the  disadvantage  that  a  comparatively  high  voltage 
is  required.  Furthermore,  the  water  coulometer  is 
not  adapted  to  the  measurement  of  large  quantities  of 
electricity. 

Titration  Coulomders.  In  the  measurement  of 
small  quantities  of  electricity  the  titration  coulometer 
is  often  useful.1  The  apparatus  is  + 

shown  in  Fig.  8.  The  vertical 
glass  tube,  fitted  at  its  lower  end 
with  a  glass  stop-cock,  is  filled  up 
to  the  dotted  line  with  a  concen- 
trated solution  of  potassium  iodide 
acidified  with  hydrochloric  acid. 
A  dilute  solution  of  hydrochloric 
acid  is  then  added  by  means  of  a 
funnel  or  pipette,  care  being  taken 
to  avoid  mixing  with  the  more 
dense  solution.  The  anode  plate 
consists  of  a  spiral  of  platinum 
wire  while  a  piece  of  platinum  foil 
serves  as  the  cathode  plate.  When 
a  current  of  electricity  passes 
thru  the  solution,  iodine  is  lib- 
erated at  the  anode,  1  equivalent 
or  126.92  grams  of  iodine  corre- 
sponding to  96500  coulombs  of 
electricity.  The  amount  of  iodine 


Fig.  8.— Titration 
coulometer. 


1  See  Danneel,  Zeit.  Elektrochem.  4,  154  (1898).      See  also 
Washburn  and  Bates,  Jour.  Am.  Chem.  Soc.,  34,  1341  (1912). 


72  ELECTROCHEMICAL  EQUIVALENTS 

set  free  is  determined  by  withdrawing  the  lower  layer 
of  the  solution  by  means  of  the  stop-cock  and  titrating 
with  a  standard  solution  of  sodium  thiosulfate  accord- 
ing to  the  well-known  procedure  of  volumetric 
analysis. 


Section  VI 

THE  ELECTRONIC  THEORY 

Electric  Discharge  in  High  Vacua.  The  recent  ad- 
vance in  our  knowledge  of  the  nature  of  electricity 
and  of  the  constitution  of  matter  is  due  hi  large 
measure  to  the  pioneer  work  of  Sir  William  Crookes 
on  the  phenomena  of  electric  discharge  hi  high  vacua. 
In  a  paper  communicated  to  the  Royal  Society  hi 
1879,  Crookes  showed  that  when  an  electric  dis- 
charge is  passed  through  a  highly  exhausted  glass 
tube,  rays  are  shot  off  from  the  cathode.  These 
"cathode  rays,"  as  they  are  called,  are  capable  of 
exciting  fluorescence  where  they  impinge  upon  the 
walls  of  the  tube ;  a  vivid  green  fluorescence  being 
developed  in  soda  glass,  and  a  blue  fluorescence  in 
potash  glass. 

The  rays  travel  hi  a  rectilinear  path  and  may  be 
brought  to  a  focus  by  means  of  a  concave  cathode. 
When  various  minerals  are  placed  at  the  focus  within 
the  exhausted  tube  they  are  rendered  fluorescent, 
while  a  piece  of  platinum  foil  can  be  rendered  in- 
candescent by  prolonged  bombardment  by  the  rays. 

It  was  Crookes'  view  that  the  rays  consist  of  a 
stream  of  electrified  molecules  of  the  residual  gas. 
In  order  to  test  the  correctness  of  this  hypothesis  he 
caused  the  rays,  after  leaving  the  cathode,  to  pass 
thru  two  parallel  slits  cut  hi  an  aluminum  dia- 
phragm, thus  giving  two  parallel  streams  of  cathode 
rays.  By  means  of  a  phosphorescent  screen  placed 

73 


74  ELECTROCHEMICAL  EQUIVALENTS 

within  the  tube  in  such  a  position  as  to  be  grazed  by 
the  rays,  then:  path  could  be  easily  traced.  It  was 
found  that  the  two  streams  of  cathode  rays  diverged ; 
that  is,  they  behaved  like  two  adjacent  streams  of 
similarly  electrified  bodies.  From  these  experiments, 
Crookes  was  led  to  consider  these  rays  as  made  up  of 
"a  fourth  or  radiant  state  of  matter."  Later  experi- 
ments by  Perrin  and  Sir  J.  J.  Thomson,  in  which  the 
rays  were  subjected  to  the  action  of  both  magnetic 
and  electrostatic  fields,  have  proved  the  rays  to 
consist  of  negatively  charged  particles. 

Velocity  of  the  Cathode  Particle.  The  velocity  of  the 
cathode  particle  was  determined  by  Thomson  in  the 
following  manner :  The  amount  of  magnetic  de- 
flection produced  by  subjecting  the  cathode  stream 
to  the  action  of  a  magnetic  field  is  proportional  to 
the  velocity,  v,  with  which  the  particles  are  moving, 
to  the  intensity  of  the  magnetic  field,  H,  and  also  to 
the  magnitude  of  the  charge,  e,  resident  upon  each 
particle.  The  corresponding  deflection  produced  by 
an  electric  field  is  proportional  to  the  intensity  of  the 
field,  X,  and  to  the  charge,  e,  on  each  particle. 
Thomson  devised  an  experiment  in  which  the  cathode 
stream  could  be  subjected  to  the  simultaneous  action 
of  both  magnetic  and  electrostatic  forces,  but  so 
arranged  that  the  effect  of  one  field  could  be  exactly 
counterbalanced  by  that  of  the  other,  thus  causing 
the  cathode  stream  to  pursue  an  undeviated,  recti- 
linear path.  A  suitable  phosphorescent  screen  served 
to  detect  any  deviation  from  the  normal  path  of  the 
particles  when  uninfluenced  by  either  magnetic  or 
electric  forces. 

When  the  magnetic  and  electric  forces  are  thus 
balanced,  we  have 

Hev  =  Xe 


ELECTRONIC  THEORY  75 

v=i 

By  means  of  this  equation,  the  velocity  of  the  cathode 
particle  may  be  calculated,  and  it  was  found  that  hi  a 
highly  exhausted  tube  this  velocity  may  be  as  high  as 
60,000  miles  per  second,  or  nearly  one-third  of  the 
velocity  of  light. 

Ratio  of  Charge  to  Mass.  Thomson  next  directed 
his  attention  to  the  determination  of  the  ratio  which 
the  electric  charge  carried  by  a  cathode  particle  bears 
to  its  mass.  He  showed  that  this  ratio  can  be  found 
by  subjecting  the  rays  to  the  action  of  an  electro- 
static field  alone.  Under  these  conditions  the  cathode 
particles  are  deflected  from  then*  rectilinear  path  hi 
exactly  the  same  way  that  a  rifle-bullet  is  deflected 
from  a  horizontal  path  and  constrained  to  fall  to  the 
earth  at  a  continually  accelerated  rate  under  the 
influence  of  the  attraction  of  gravitation. 

In  the  case  of  a  cathode  particle,  its  acceleration 
will  be  directly  proportional  to  the  strength  of  the 
field,  X,  to  its  charge,  e,  and  inversely  proportional  to 
its  mass,  m.  Or,  expressing  these  facts  hi  mathe- 
matical language,  we  have 

Acceleration  = — 
m 

The  science  of  Mechanics  teaches,  that  the  distance 
thru  which  a  body  will  fall  freely  under  the  in- 
fluence of  gravity  hi  a  tune  t,  is  1/2  gt2,  where  g  is  the 
acceleration  due  to  gravity.  Similarly,  the  deflection 
of  the  cathode  stream  under  the  influence  of  the 
electrostatic  field,  X,  as  shown  by  the  displacement 
of  the  luminous  spot  on  the  phosphorescent  screen, 
will  be 


76  ELECTROCHEMICAL  EQUIVALENTS 


m 


Since  t  =  1/v,  where  t,  1,  and  v  denote  time,  distance, 
and  velocity  respectively,  we  may  replace  t2  in  the 
above  expression  for  displacement  by  !2/v2,  when  we 
have 

d-1    XeP 
~*'  rn^ 

or 

e  =  2d  v2 

m     X  I2 

In  this  last  equation  all  of  the  terms  on  the  right- 
hand  side  of  the  equality  sign  are  susceptible  of  direct 
measurement. 

Thomson  found  that  the  ratio  e/m  is  the  same  for 
all  cathode  rays  provided  they  are  not  moving  with 
velocities  of  the  same  order  of  magnitude  as  the  veloc- 
ity of  light.  He  also  found  that  the  ratio  is  indepen- 
dent of  the  nature  of  the  residual  gas  in  the  tube 
and  likewise  of  the  chemical  nature  of  the  electrodes. 
The  value  of  e/m,  expressed  hi  electrostatic  units,  is 
5.1  x  1017.  The  largest  value  of  e/m  hitherto  known 
was  that  for  the  hydrogen  ion  in  electrolysis,  where 
the  ratio  of  charge  to  mass,  expressed  in  electrostatic 
units,  is  3  x  1014.  Therefore,  for  the  cathode  par- 
ticle, the  ratio  is  1700  times  greater  than  the  cor- 
responding ratio  for  the  hydrogen  ion  in  electrolysis. 
It  is  evident  that  this  may  be  due  to  the  charge 
being  1700  tunes  greater  than  the  charge  on  the 
hydrogen  ion  in  electrolysis  (the  mass  of  the  ion  and 
that  of  the  cathode  particle  being  assumed  equal),  or, 
to  the  mass  of  the  cathode  particle  being  only  1/1700 
of  the  mass  of  that  of  the  hydrogen  ion  (the  charges 
being  assumed  the  same). 


ELECTRONIC  THEORY  77 

Magnitude  of  the  Charge,  e.  It  is  a  familiar  fact 
that  fogs  are  due  to  the  condensation  of  water  vapor 
on  dust  particles  in  the  atmosphere,  each  particle  of 
dust  acting  as  the  nucleus  around  which  a  droplet  of 
water  can  form.  On  cooling  a  mass  of  air  which  has 
been  completely  freed  from  dust,  no  fog  will  be 
formed  because  there  are  no  nuclei  upon  which  water 
vapor  can  condense.  Air  in  this  condition  is  said  to  be 
"supersaturated,"  i.e.,  it  holds  more  than  the  normal 
amount  of  moisture  for  that  particular  temperature. 
If  a  little  dust  be  introduced  into  supersaturated  air, 
an  immediate  condensation  to  fog  occurs.  It  has 
been  shown  by  C.  T.  R.  Wilson  that  if  a  vessel  be 
filled  with  air  from  which  all  dust  particles  have  been 
removed  by  filtration  through  cotton-wool,  it  is  possi- 
ble to  cool  it  to  such  an  extent  that  it  will  hold  in 
suspension  fully  eight  times  the  amount  of  water 
vapor  it  should  normally  contain.  On  further  cooling, 
the  moisture  precipitates  in  the  form  of  rain. 

Wilson  also  discovered  that  cathode  particles  serve 
as  nuclei  for  the  condensation  of  moisture  from  super- 
saturated air,  and  that  condensation  occurs  at  a 
temperature  corresponding  to  a  fourfold  saturation. 
By  enclosing  a  mass  of  dust-free  air  in  a  glass 
chamber  closed  by  a  piston*  the  desired  degree  of 
supersaturation  can  be  obtained  by  withdrawing  the 
piston,  thus  expanding  the  air  and  lowering  its  temper- 
ature. If  cathode  rays  are  then  permitted  to  enter 
the  chamber,  a  fog  immediately  results,  and  by 
proper  adjustment  of  the  expansion,  it  is  possible  to 
estimate  the  actual  weight  of  water  condensed. 

Having  determined  the  total  weight  of  condensed 
moisture,  it  is  evident  that  a  knowledge  of  the  average 
volume  of  a  single  drop  would  make  possible  the 
calculation  of  the  total  number  of  drops,  and,  on  the 


78  ELECTROCHEMICAL  EQUIVALENTS 

reasonable  assumption  that  each  drop  is  associated 
with  but  one  cathode  particle,  the  number  of  such 
particles  would  be  known.  The  volume  of  a  single 
drop  can  be  computed  by  means  of  a  formula  derived 
by  Sir  George  Stokes  for  the  velocity  of  fall  of  a 
minute  spherical  body  in  terms  of  its  radius,  r,  and 
the  viscosity,  ??,  of  the  medium  in  which  it  falls. 
Stokes'  formula  is 


where  u  denotes  the  velocity  of  fall  of  the  body  and 
g  is  the  acceleration  due  to  gravity.  By  noting  the 
velocity  with  which  the  fog  settles  in  the  expansion 
chamber,  the  value  of  r  in  the  foregoing  formula  may 
be  calculated. 

Having  calculated  the  total  number  of  cathode 
particles,  by  dividing  the  total  weight  of  water  con- 
densed by  the  volume  of  a  single  drop,  4/3  •*  r3,  it  only 
remains  to  measure  the  total  quantity  of  electricity 
on  the  precipitated  water  vapor  in  order  to  ascertain 
the  charge  on  each  particle.  The  charge  on  a  single 
cathode  particle  was  thus  found  to  be  3.1  x  1(H° 
electrostatic  units.  Recent  improvements  in  Wilson's 
method  have  enabled  Millikan1  to  determine  the 
value  of  e  with  extreme  accuracy.  Millikan  assigns 
to  e  the  value  4.4775  x  KH0  electrostatic  units,  the 
error  not  exceeding  1  part  in  1000. 

These  cathode  particles  were  at  first  called  cor- 
puscles but  they  are  now  commonly  known  as  elec- 
trons. The  electron  appears  to  be  nothing  but  an 
isolated  charge  of  negative  electricity.  All  electrons 
are  alike,  being  entirely  independent  of  the  particular 

1  Millikan,  Phil.  Mag.  IV,  19,  209  (1910)  ;  Phys.  Rev.  32,  349 
(1911)  ;  Trans.  Am.  Electrochem.  Soc.,  21,  185,  (1912). 


ELECTRONIC  THEORY  79 

atom  from  which  they  may  have  escaped.  This  leads 
to  the  view  that  electricity,  like  matter,  is  made  up  of 
discrete  particles  analogous  to  atoms.  An  electron 
may  be  defined  as  a  minute  particle  having  an  ap- 
parent mass  of  about  1/1700  that  of  the  atom  of  hydro- 
gen and  carrying  a  negative  charge  of  electricity 
equal  to  4.4775  x  10~10  electrostatic  units. 

Other  Sources  of  Electrons.  Cathode  rays  are  not 
the  only  source  of  electrons.  Electrons  are  given  out 
by  radio-active  substances,  by  metals,  and  by  some 
amalgams  when  heated  or  exposed  to  light,  especially 
to  ultra-violet  light,  and  also  by  gas  flames  charged 
with  the  vapors  of  salts.  Whatever  the  source  from 
which  the  electrons  may  be  derived,  the  value  of  the 
ratio,  e/m,  remains  constant.  The  constancy  of  this 
ratio  led  Sir  J.  J.  Thomson  to  say  that  the  electron 
is  to  be  regarded  "as  one  of  the  bricks  of  which 
atoms  are  built  up." 

Structure  of  the  Atom.  According  to  Thomson,  the 
atom  of  any  element  is  assumed  to  consist  of  an  as- 
semblage of  negatively  charged  particles  or  electrons, 
held  together  by  a  positively  charged  nucleus,  the 
amount  of  positive  electricity  being  equivalent  to  the 
total  negative  charge  of  the  electrons.  At  the  present 
time  little  definite  information  exists  as  to  this  positive 
nucleus,  beyond  the  fact  that  carriers  of  positive 
electricity  possess  masses  which  are  comparable  with 
the  mass  of  the  atom  of  hydrogen.  A  small  number 
of  electrons  near  the  surface  or  outer  shell  of  the 
atom  are  believed  to  possess  a  greater  degree  of 
freedom  and  to  be  less  firmly  held  than  those  nearer 
the  positive  nucleus.  These  electrons  are  known  as 
the  valence  electrons,  since  their  number  determines 
the  maximum  valence  of  the  atom. 

While  further  discussion  of  atomic  structure  lies 


80  ELECTROCHEMICAL  EQUIVALENTS 

beyond  the  scope  of  this  book  yet  mention  should  be 
made  of  the  recent  theory  of  Nicholson.1  According 
to  Nicholson  the  positive  residue  of  the  atom  exists 
hi  the  form  of  separate  masses,  each  of  uniform 
density  and  having  diameters  which  are  relatively 
small  in  comparison  with  the  diameters  of  the  elec- 
trons. Nicholson  says,  "In  a  complex  atom,  built  up 
of  simpler  systems,  the  assemblage  of  positive  charges 
is  hi  many  respects  similar  to  the  assemblage  of 
electrons  which  revolve  around  them,  and  it  is  not 
unlikely  that  many  of  the  positive  charges  would  also 
revolve.  But  they  are  not  all  of  the  same  size, 
although  the  difference  hi  size  is  not  great.  Then* 
mass  is  so  great  that  a  disturbance  which  could  expel 
one  of  them  from  an  atom  would  also  expel  many  of 
the  attendant  electrons,  and  it  would  be  impossible 
to  isolate  a  positive  charge." 

The  Electron  and  the  Chemical  Elements.  While  the 
hypothetical  atom  of  Thomson  undoubtedly  bears  but 
a  remote  resemblance  to  the  real  atom,  and  while  as 
Thomson  has  pointed  out,  there  are  many  imperfec- 
tions in  his  theory,  it  nevertheless  sheds  a  most 
interesting  light  on  the  mutual  relationships  of  the 
chemical  elements  and  then*  differences  in  valence  or 
combining  power. 

Thomson  has  calculated  the  possible  distribution  of 
negative  electric  charges  within  a  sphere  of  positive 
electricity  of  uniform  density.  When  the  presence  of 
only  one  electron  is  assumed,  it  necessarily  goes  to 
the  center  of  the  sphere.  Where  a  larger  number  are 
assumed  to  be  present  the  calculation  has  been 
confined  to  those  cases  hi  which  the  electrons  lie  in  a 
plane  passing  thru  the  center  of  the  sphere.  The 

1  Nicholson,  Phil.  Mag.  IV,  22,  864  (1911). 


ELECTRONIC  THEORY  81 

maximum  number  of  electrons  which  can  be  in  equi- 
librium in  a  single  ring  is  5.  In  order  to  increase  the 
number  of  electrons  in  a  ring  it  is  necessary  to  place 
some  of  them  within  the  ring.  Thus,  though  a  ring 
containing  6  equally  spaced  electrons  is  unstable 
alone,  it  immediately  acquires  stability  if  1  electron 
is  placed  at  the  center  of  the  ring.  A  system  involv- 
ing a  greater  number  of  electrons  will  arrange  itself 
in  a  series  of  concentric  rings,  the  number  of  electrons 
in  successive  rings  decreasing  as  the  center  is  ap- 
proached. The  accompanying  table  shows  the  num- 
bers of  electrons  from  1  to  69,  arranged  in  rings,  the 
first  line  showing  the  numbers  which  may  fall  into 
one  ring,  the  second  line  the  numbers  which  may  give 
rise  to  two  rings,  the  third  line  those  which  form  three 
rings,  and  so  on. 

NUMBERS   OF  ELECTRONS  IN   CONCENTRIC    RINGS 
12345 

5     6     7     8     8     8    9  10  10  10  11 
11112333455 

11  11  11  12  12  12  13  13  13  13  13  14  14  15  15 
5  6  7  7  8  8  8  8  9  10  10  10  10  10  11 
11111233334455  '5 

15  15  15  16  16  16  16  16  16  16  17  17  17  17  17  17  17 

11  11  11  11  12  12  12  13  13  13  13  13  13  14  14  15  15 

5  6  7  7  7  8  8  8  8  9  9  10  10  10  10  10  11 

11111122333344555 

17  18  18  18  18  18  19  19  19  19  20  20  20  20  20  20  20  20  20  21  21 

15  15  15  15  16  16  16  16  16  16  16  16  16  17  17  17  17  17  17  17  17 

11  11  11  11  11  12  12  12  12  13  13  13  13  13  13  13  14  14  15  15  15 

5  5  6  7  7  7  7  8  8  8  8  8  9  9  10  10  10  10  10  10  11 

111111112223333445555 

It  will  be  observed  that  the  numbers  in  the  same 
vertical  columns  of  the  table  are  repeated  in  each 
series,  the  number  of  electrons  in  the  outer  ring 
forming  the  top  line.  For  example,  in  the  first 


82  ELECTROCHEMICAL  EQUIVALENTS 

column  of  the  first  series,  we  find  the  numbers  5,  1 ; 
in  the  next  series  we  find  the  numbers  11,  5,  1 ;  in 
the  next  series  we  find  the  numbers  15,  11,  5,  1 ;  and 
in  the  last  series  we  find  the  numbers  17,  15,  11,  5,  1. 

The  bearing  of  this  table  on  the  natural  grouping  of 
the  chemical  elements  may  be  illustrated  by  consider- 
ing the  properties  of  all  configurations  having  20 
electrons  in  the  outer  ring.  The  smallest  number  of 
electrons  in  a  system  having  20  electrons  in  the  outer 
ring  is  59.  In  this  case  the  number  of  electrons 
within  is  only  just  sufficient  to  impart  stability  to  the 
ring,  any  slight  disturbance  being  able  to  cause  the 
loss  of  1  electron.  Should  this  occur  the  residue 
would  acquire  a  positive  charge  and  the  resulting 
atom,  containing  58  electrons,  would  resemble  in  its 
properties  a  univalent  positive  element.  When  we 
pass  from  59  to  60  electrons,  the  outer  ring  acquires 
greater  stability  owing  to  the  presence  of  an  additional 
electron  within  the  system.  Similarly,  the  system 
containing  61  electrons  is  even  more  stable  than  that 
containing  60  electrons.  The  stability  continues  to 
increase  until  the  number  of  electrons  in  the  atom 
reaches  67,  when  the  addition  of  another  electron 
destroys  the  stability  of  the  system,  since  it  enters 
the  outer  ring,  thus  increasing  the  number  of  elec- 
trons to  21,  and  producing  a  configuration  favoring  the 
detachment  of  an  electron,  as  in  the  case  of  the 
system  containing  59  electrons. 

It  will  be  observed  that  the  change  from  59  to  67 
electrons,  produced  by  the  successive  additions  of  a 
single  electron,  corresponds  to  the  addition  of  8 
negative  charges.  The  system  containing  60  electrons 
will  be  the  most  positive  of  the  series.  It  can  give  up 
1  electron,  but  only  1,  since  if  it  were  to  give  up  2,  a 
system  of  58  electrons  woulcl  result,  similar  to  that 


ELECTRONIC     THEORY  83 

obtained  by  the  removal  of  an  electron  from  an  atom 
containing  59  electrons.  Such  a  system  would 
acquire  two  positive  charges  of  electricity  and  would 
possess  even  greater  attraction  for  external  electrons. 
Therefore,  since  the  atom  containing  60  electrons  can 
carry  but  one  positive  charge  it  will  resemble  in  its 
behavior  a  univalent  positive  element. 
Turning  our  attention  now  to  the  system  containing 

67  electrons,   we   find   that  the   outer  ring  is  very 
stable,  and,  as  we  have  seen,  the  addition  of  1  elec- 
tron would  involve  a  rearrangement  resulting  in  a 
system  having  21  electrons  hi  the  outer  ring.     Since 

68  is  the  minimum  number  of  electrons  which  can 
exist  under  these  conditions  with  an  outer  ring  of  21, 
it  follows  that  an  electron  may  readily  be  lost.    The 
resulting   configuration   of   67    electrons,    after   thus 
acquiring  a  negative  charge,  would  immediately  lose 
it  again,  and  the  system  would  thus  be  incapable  of 
retaining    any    permanent    charge.    Its    behavior    is 
quite  analogous  to  the  rare  gases  which  are  known  to 
be   inactive   chemically.    The   system   containing   66 
electrons  can  retain  but  a  single  negative  charge ; 
for  should  2  electrons  be  added  to  it,  a  configuration 
involving   68   electrons   would   result,   and   that   has 
already   been   seen   to   lose    electrons   easily.    This 
system  then  resembles  in  its  properties  a  univalent 
negative  element. 

Proceeding  in  a  similar  manner,  successively  in- 
creasing the  number  of  electrons,  we  obtain  systems 
corresponding  to  univalent,  divalent,  and  trivalent, 
positive  elements  at  one  end  of  the  series,  and 
trivalent,  divalent,  and  univalent,  negative  elements 
at  the  other  end  of  the  series.  This  is  analogous  to 
the  familiar  arrangement  of  the  chemical  elements  due 
to  Mendeleef ,  shown  hi  part  in  the  following  table  : 


84  ELECTROCHEMICAL  EQUIVALENTS 

He      Li       Be       B       C       N      O      F       Ne 

Ne      Na      Mg      Al      Si      P       S       Cl      A 

When  atoms  in  which  the  outer  rings  have  a  high 
stability  are  brought  in  close  proximity  to  other  atoms 
in  which  the  electrons  are  less  firmly  held,  an  ex- 
change of  electrons  may  occur.  In  this  interchange 
the  electropositive  atoms  will  acquire  a  positive 
charge,  and  the  electronegative  atoms  a  negative 
charge.  The  resulting  oppositely  charged  atoms  will 
then  unite  to  form  a  chemical  compound. 

The  Electronic  Conception  of  Valence.  Sir  William 
Ramsay  has  put  forward  the  following  hypothesis  l :  — 
"Electrons  are  atoms  of  the  chemical  element,  elec- 
tricity; they  possess  mass,  they  form  compounds 
with  other  elements;  they  are  known  in  the  free 
state,  that  is  as  molecules ;  they  serve  as  the  bonds 
of  union  between  atom  and  atom."  According  to 
this  hypothesis,  when  common  salt  is  dissolved  in 
water  and  undergoes  ionization  into  Na  and  Cl'  ions, 
the  Na  ion  is  to  be  regarded  as  an  atom  of  sodium 
minus  an  electron,  and  the  Cl'  ion  as  an  atom  of 
chlorine  plus  an  electron.  That  is,  the  sodium  atom 
may  be  thought  of  as  a  compound  of  the  Na  ion  with 
an  electron,  whereas  the  Cl'  ion  may  be  regarded  as  a 
compound  of  the  chlorine  atom  with  an  electron. 
Ramsay  represents  the  union  between  sodium  and 
chlorine  by  the  equation 

ENa  +  Cl  =  NaECl 

where  the  symbol  E  denotes  the  electron.    It  is  the 
electron,  hi  other  words,  that  serves  as  the  connecting 
link  between  the  atoms  of  sodium  and  chlorine, - 
it  is  another  way  of  representing  combining  capacity 

1  Ramsay,  Jour.  Chem.  Soc.,  93,  778  (1908). 


ELECTRONIC  THEORY  85 

or  valence.  We  may  then  define  the  valence  of  an 
element  as  the  number  of  electrons  which  the  element 
loses  or  gains  to  form  chemical  bonds.  The  forma- 
tion of  a  chemical  bond  or  linkage  between  two  atoms 
necessarily  involves  the  transfer  of  an  electron  from 
one  atom  to  another,  and  this  transfer  imparts  a 
negative  charge  to  the  atom  which  gains  the  electron, 
and  a  positive  charge  to  the  atom  which  loses  the 
electron. 

The  Electronic  Conception  of  Conductance.  As  has 
been  pointed  out,  conductors  of  electricity  may  be 
conveniently  divided  into  two  classes;  the  metals 
and  carbon  forming  the  first  class,  and  dissolved  or 
fused  electrolytes  the  second  class.  The  mechanism 
of  electrical  conductance,  whether  metallic  or  elec- 
trolytic, may  be  satisfactorily  explained  in  terms  of 
the  electronic  hypothesis.  Thus,  when  a  difference  of 
potential  is  established  between  the  ends  of  a  metallic 
conductor,  a  stream  of  electrons  immediately  begins 
to  flow.  This  electronic  stream  constitutes  the  elec- 
tric current  in  the  metal  and  the  rise  of  temperature 
incident  to  the  passage  of  the  current  is  to  be  ascribed 
to  the  heat  developed  by  the  collision  of  the  electrons 
with  the  atoms  of  metal.  Since  the  electric  current 
is  to  be  regarded  as  a  stream  of  negatively  charged 
carriers  of  electricity,  we  are  forced  to  define  the 
"  direction  of  the  current "  in  a  metallic  conductor  as 
opposite  to  that  in  which  the  electricity  really  flows. 

In  conductors  of  the  second  class  the  ions  of  the 
electrolyte  carry  the  current,  each  kind  of  ion  par- 
ticipating in  proportion  to  its  current-carrying  capacity. 
Since  in  the  metallic  portion  of  the  circuit,  including 
the  electrodes,  the  current  consists  of  a  stream  of 
electrons,  it  follows  that  at  the  electrode  surfaces 
there  must  be  an  exchange  of  electrons  between  the 


86  ELECTROCHEMICAL  EQUIVALENTS 

electrodes  and  the  ions  of  the  electrolyte.  This  ex- 
change of  electrons,  commonly  called  an  electro- 
chemical reaction,  generally  involves  only  those  ions 
which  most  readily  gain  or  lose  electrons  under  the 
conditions.  It  has  been  shown  hi  the  preceding 
section  that  the  liberation  or  solution  of  one  equiva- 
lent weight  of  a  substance  requires  approximately 
96500  coulombs  of  electricity.  It  is  evident  that  if 
the  number  of  atoms  contained  in  one  gram-atom  of 
an  element  were  known,  it  would  be  possible  to 
calculate  the  number  of  coulombs  carried  by  one 
electron.  It  has  recently  been  shown  by  Perrin  that 
the  probable  number  of  atoms  in  one  gram-atom  of 
an  element  is  68.5  x  1022;  assuming  this  number  to 
be  correct,  we  have 


and    multiplying    by    3  x  109,    in    order    to    convert 
coulombs  into  electrostatic  units,  we  have 

96500  x  3  x  109 
e  — 


68.5  x  1022 
or 

e  =  4.227  x  10~10  electrostatic  units 

On  comparing  this  result  with  Millikan's  value  for 
e,  viz.,  4.4775  x  10~10,  it  will  be  observed  that  the 
agreement  is  all  that  could  be  desired.  The  electro- 
chemical constant  or  faraday  is  thus  seen  to  be  equal 
to  the  product  of  the  charge  on  the  electron  and  the 
number  of  atoms  in  one  atomic  weight  of  an  element, 

The  following  references  are  given  for  the  benefit 
of  those  who  may  desire  to  gain  more  detailed  in- 
formation on  various  phases  of  the  electronic  theory : 


ELECTRONIC  THEORY  87 

"  The  Discharge  of  Electricity  through  Gases,"  by 

J.  J.  Thomson, 
"  Conduction  of  Electricity  through  Gases,"  by  J.  J. 

Thomson, 

11  Electricity  and  Matter,"  by  J.  J.  Thomson, 
"The     Corpuscular   Theory    of    Matter,"    by    J.  J. 

Thomson, 

"  Beyond  the  Atom,"  by  J.  Cox, 
"Elements  and  Electrons,"  by  William  Ramsay, 
11  The  Theory  of  Valency,"  by  J.  Newton  Friend, 
"The  Nature  of  Matter  and  Electricity,"  by  Comstock 

and  Troland. 


APPENDICES 


Appendix  1 

VALENCE 

Textbooks  and  different  authorities  use  both  the 
terms  "  valence"  and  "valency"  in  different  ways 
and  sometimes  rather  vaguely ;  nor  is  there  agree- 
ment as  to  the  precise  physical  conceptions  repre- 
sented by  them.  In  electrochemistry  that  which  is 
represented  by  them  has  an  important  significance 
and  they  ought  to  be  clearly  understood  and  used 
with  definite  meanings.  When  the  numerical  value 
of  a  valence  is  unity,  as  it  is  with  hydrogen  and  a  few 
other  elements,  it  naturally  falls  out  of  the  calcula- 
tions and  is  thereby  lost  sight  of,  but  in  all  other  cases 
it  is  a  very  important  factor,  for  when  the  valence  is 
twice  as  great  in  one  case  as  in  another,  the  amount 
of  electricity  required  to  produce  the  chemical  change 
will  be  twice  as  great. 

When  the  chemist  refers  to  the  "  chemical  equiva- 
lents "  of  two  elements,  the  valence  has  already  been 
taken  into  account  and  therefore  is  not  given  as  an 
additional  factor  and  is  lost  sight  of.  Thus  the 
chemical  equivalents  of  zinc  (valence  2)  and  hydrogen 
(valence  1)  are  65.37  (the  atomic  weight  of  zinc)  and 
2.016  (twice  the  atomic  weight  of  hydrogen)  when  they 
are  given  with  reference  to  zinc ;  or  32.69  (half  the 
atomic  weight  of  zinc)  and  1.008  when  stated  with 
reference  to  hydrogen ;  the  ratios  of  course  are  the 
same  in  both  cases.  In  these  ratios  the  weights  have 
both  been  reduced  to  the  same  valence,  hence  the 
valence  need  then  no  longer  be  stated.  The  chemist 

91 


92  ELECTROCHEMICAL  EQUIVALENTS 

therefore  often  eliminates  the  valence  by  referring 
directly  to  the  "  chemical  equivalents  "  ;  but  in  many 
electrochemical  calculations  the  consideration  of  the 
valence  as  a  separate  factor  so  greatly  simplifies  many 
of  the  calculations  that  it  is  generally  worth  while 
doing  so,  and  it  enables  a  table  of  equivalents  such  as 
the  one  in  this  book  to  be  prepared  for  different 
valences,  thereby  often  saving  the  worst  parts  of  the 
calculations.  Those  who  prefer  to  use  chemical 
equivalents  (in  which  the  valence  has  already  been 
included)  will  have  to  make  the  electrochemical 
calculations  for  hydrogen  or  some  other  element,  and 
then  by  means  of  the  chemical  equivalents  determine 
from  this  the  corresponding  amount  of  the  element 
in  the  problem ;  this  involves  a  double  calculation. 

Chemists  do  not  seem  to  be  in  agreement  either  as 
to  whether  the  same  physical  conception  of  valence 
applies  equally  well  to  all  branches,  like  organic 
chemistry  and  electrolysis.  It  is  believed  by  the 
writer  however  that  the  following  conception  of  val- 
ence is  in  substantial  agreement  with  the  generally 
accepted  electronic  theory,  that  it  can  safely  be  applied 
at  least  to  all  electrochemical  reactions,  and  that  when 
properly  used  in  calculations  it  will  always  give  the 
correct  results.  This  conception  will  greatly  simplify 
many  electrochemical  calculations,  and  it  is  believed 
will  also  give  a  clearer  understanding  of  the  reactions. 
It  serves  at  least  as  a  useful  and  reliable  working 
tool  in  electrochemistry  independently  of  whether  or 
not  it  applies  equally  well  to  non-electrolytes  or  or- 
ganic chemistry. 

Bonds.  When  two  different  elements  are  chemi- 
cally combined  to  form  a  compound,  it  is  convenient 
to  consider  the  force  or  affinity  which  holds  them 
together  to  be  represented  by  chemical  bonds.  In 


VALENCE  93 

electrolytes  these  bonds,  or  at  least  some  of  them, 
are  of  such  a  nature  that  they  may  be  broken  or 
created  by  an  electric  current.  The  greater  the 
number  of  such  bonds  the  greater  is  the  quantity  of 
electricity  which  is  required,  hence  it  is  convenient 
for  calculations  to  specify  some  unit  bond  in  terms 
of  which  their  number  can  be  measured  and 
specified. 

Unit  bond.  The  faraday.  For  convenience  this 
unit  bond  is  conventionally  assumed  to  be  the  one 
combining  a  gram-atom  of  hydrogen  (1.008  grams) 
with  other  elements,  and  by  experiment  it  has  been 
found  that  it  requires  a  passage  of  96,494  coulombs 
of  electricity  to  break  or  create  this  unit  bond.  This 
quantity  or  charge  of  electricity  is  now  by  general 
consent  called  a  faraday  and  is  usually  abbreviated  to 
96,500  coulombs;  it  may  often  be  more  convenient 
to  use  its  equivalent  26.804  ampere-hours. 

In  the  generally  accepted  electronic  theory  it  is 
supposed  that  each  gram-ion  carries  a  charge l  of  this 
amount  thru  the  electrolyte  from  one  electrode  to  the 
other,  thereby  transmitting  the  current,  as  explained 
in  Part  n.  It  is  where  this  charge  is  received  or 
discharged,  namely  at  the  electrodes,  that  the  chemi- 
cal reactions  are  apparent.  From  Faraday's  law  it 
follows  that  in  electrolysis  this  bond  has  the  same 
value  when  expressed  electrically  for  a  gram-ion  of 
any  element,  hence  it  serves  well  as  a  unit  in  terms 
of  which  the  bonds  between  elements  can  be  ex- 
pressed or  measured. 

Definition  of  valence.  This  leads  to  the  definition 
of  valence,  which  may  be  said  to  be  the  number  of 

lUAn  Enlarged  Electron  of  Practical  Size:  The  Faraday," 
by  Carl  Hering,  Met.  and  Chem.  Engineering,  May  15,  1917, 
p.  598- 


94  ELECTROCHEMICAL  EQUIVALENTS 

these  unit  bonds  which  each  gram-atom  has  when  in 
combination  with  other  elements.  Or  expressed  elec- 
trically, valence  may  be  said  to  be  the  number  of 
charges,  in  faradays,  which  each  gram-atom  then 
carries.  This  definition  applies  at  least  to  electrolytes 
and  is  therefore  sufficient  for  electrochemical  calcula- 
tions ;  it  is  also  believed  to  be  the  simplest  and  most 
useful  conception  of  valence  for  use  in  electro- 
chemistry ;  whether  it  applies  also  to  non-electrolytes 
and  to  organic  chemistry  is  perhaps  still  open  to 
controversy." l 

Thus  in  one  gram-molecule  of  water,  H2O,  consist- 
ing of  two  gram-atoms  of  hydrogen  and  one  of 
oxygen,  there  must  be  two  such  unit  bonds  uniting 
those  elements,  as  each  one  of  the  two  gram-atoms  of 
hydrogen  has  one  by  definition,  that  is,  hydrogen  has 
a  valence  of  1 ;  therefore  the  single  gram-atom  of 
oxygen  must  be  said  to  have  two  such  bonds,  hence 
its  valence  is  2.  One  gram-molecule  of  water,  18.016 
grams,  therefore  requires  two  faradays  or  53.6  ampere- 
hours,  to  break  its  two  bonds. 

A  bond  always  joins  two  elements,  but  it  may  be 
considered  with  reference  to  either  of  them,  as  it  is 
in  this  definition  of  valence.  Thus  in  the  above  with 
reference  to  the  hydrogen  there  is  one  bond  per  atom, 
hence  its  valence  is  1,  but  with  reference  to  the 

1  Alexander  Smith  in  his  "General  Inorganic  Chemistry" 
gives  the  following  definition :  "  The  valence  of  the  atomic  weight 
of  an  element  is  the  number  of  atomic  weights  of  hydrogen,  or 
of  some  other  univalent  element,  which  it  combines  with  or 
displaces." 

J.  W.  Mellor  in  his  "  Modern  Inorganic  Chemistry  "  gives  the 
following  definition :  "  The  valency  of  an  element  is  a  number 
which  expresses  how  many  atoms  of  hydrogen,  or  of  other 
atoms  equivalent  to  hydrogen,  can  unite  with  one  atom  of  the 
element  in  question." 


VALENCE  95 


single  atom  of  oxygen  there  are  two  bonds  per  atom, 
hence  its  valence  is  2. 

Ordinarily  valences  are  always  whole  numbers 
running  from  1  to  about  8 ;  elements  with  valences 
of  1,  2,  3,  etc.,  are  called  mono-valent,  di-valent,  tri- 
valent,  etc.;  elements  like  the  noble  gases  which 
seem  never  to  combine  with  any  other  element  are 
best  called  non-valent,  instead  of  zero-valent,  for 
reasons  given  below.  Much  higher  valences  have 
been  claimed  to  exist,  as  also  fractional  ones,  but  it  is 
probably  safe  to  say  that  neither  occur  in  electrolysis, 
or  at  least  very  rarely. 

Non-electrolytic  bond.  Sometimes  a  bond  joins  two 
atoms  of  the  same  element ;  a  molecule  of  hydrogen 
gas  for  instance  is  for  good  reasons  considered  to  be 
composed  of  two  atoms  combined  together,  that  is,  it 
is  diatomic.  Molecules  of  some  elements  have  three  or 
four  atoms.  Such  bonds  are  also  assumed  to  exist  in 
some  compounds  as  expressed  hi  so-called  structural 
formulas,  like  the  one  between  the  two  O's  in  H-O-O-H 
for  instance.  But  the  writer  believes  it  is  safe  to 
say  that  these  bonds  have  no  equivalence  in  faradays 
and  never  seem  to  enter  into  any  electrochemical 
calculations ;  all  such  calculations  for  the  usual  cases 
seem  to  agree  reliably  with  experiment  when  the 
making  or  breaking  of  this  kind  of  bond  is  ignored; 
Faraday's  law  does  not  refer  to  them ;  it  is  believed 
to  be  impossible  ever  to  set  free  the  same  element  at 
both  electrodes,  which  would  mean  breaking  this 
kind  of  a  bond  electrically.  Hence  with  our  present 
knowledge  it  seems  safe  to  consider  this  kind  of 
bond  to  differ  physically  from  the  one  combining 
different  elements,  at  least  to  the  extent  that  it  may 
be  ignored  in  electrochemical  calculations  occurring  in 
practice  as  far  as  any  equivalent  in  faradays  is  con- 


96  ELECTROCHEMICAL  EQUIVALENTS 

cerned.  Structural  formulas  are  employed  chiefly 
for  compounds  which  are  not  electrolytes  and  there- 
fore not  subject  to  electrochemical  calculations. 

By  using  the  change  of  valence  based  on  the  usual 
chemical  formulas,  instead  of  the  valence  itself,  as 
described  below,  it  is  believed  that  no  errors  will 
arise  in  neglecting  this  kind  of  bond  in  electro- 
chemical calculations.  In  electrolyzing  a  gram-mole- 
cule of  water,  H2O,  it  is  well  recognized  and  proved 
by  experiment  that  it  requires  two  faradays,  which 
means  that  there  were  two  bonds ;  yet  in  the  gaseous 
hydrogen  formed  there  are  two  atoms  to  the  molecule, 
hence  there  must  be  a  bond  connecting  them ;  this 
bond  was  evidently  not  included  in  stating  that  the 
valence  of  hydrogen  is  1  and  that  of  oxygen  2,  nor  is 
it  concluded  in  the  chemical  formula  for  water. 
Whether  it  originated  during  electrolysis  or  existed  in 
the  water  is  perhaps  not  yet  known,  but  it  is  known 
that  it  does  not  enter  into  electrochemical  calculations 
of  this  kind. 

In  a  compound  consisting  of  more  than  two  ele- 
ments, like  H2SO4  for  instance,  the  current  cannot 
break  it  into  more  than  two  parts,  hence  one  part 
(one  of  the  ions)  must  contain  several  elements,  hi 
this  case  it  is  SO4  as  the  current  always  breaks  the 
bond  between  the  H2  and  the  SO4  instead  of  the  one 
between  the  S  and  the  O4.  It  does  not  necessarily  fol- 
low from  this  that  the  bonds  between  the  S  and  the  O 
are  not  electrolytic  ;  they  may  merely  be  the  stronger 
of  the  two ;  in  fact  it  is  said  to  be  possible  to  break  these 
bonds  electrolytically  also,  obtaining  free  sulfur. 

But  the  kind  of  bond  joining  two  atoms  of  the 
same  element  seems  to  be  physically  different  and  is 
not  included  among  those  referred  to  in  this  book  as 
being  represented  by  a  faraday. 


VALENCE  97 

Zero  valence.  If  the  valence  represents  the  number 
of  bonds  in  a  combination  each  of  which  are  equiva- 
lent to  a  faraday,  it  follows  that  the  elements  can 
have  no  valence  when  they  are  in  their  free  uncom- 
bined  state  as  there  are  then  no  bonds.  That  is,  the 
valence  of  any  element  in  its  free  state  must  neces- 
sarily be  considered  to  be  zero.  This  term  is  some- 
times applied  to  those  elements  like  the  inert  gases 
which  never  enter  into  any  combinations,  that  is,  they 
never  have  any  valences.  It  is  preferable  to  distin- 
guish between  these  two  cases  by  saying  that  the 
latter  are  non-valent,  as  hi  electrochemistry  it  is  very 
convenient  and  sometimes  quite  necessary  to  be  able 
to  refer  to  the  free  or  uncombined  state  of  an  element 
as  one  in  which  it  has  a  zero  valence. 

Valence  vs.  valency.  For  this  and  other  reasons  it 
is  very  desirable  to  make  a  distinction  between  the 
terms  valence  and  valency,  which  formerly  have  been 
used  rather  indiscriminately,  thereby  causing  con- 
fusion. The  writer  recommends  l  limiting  the  term 
" valence"  as  above  described  to  represent  the  number 
of  bonds  per  atom  which  the  element  has  in  any  specific 
combination,  and  to  limit  the  term  "valency"  to 
express  the  properly  which  an  element  has  to  combine 
with  others  in  various  proportions.  Thus  copper  for 
instance  is  then  said  to  possess  the  property  of  having 
a  valency  of  1  and  2 ;  and  when  combined  in  the 
specific  combination  of  cuprous  chloride  its  valence  is 
1,  while  hi  cupric  chloride  its  valence  is  2 ;  and  in  its 
free  state  as  metal  its  valence  is  0. 

Change  of  valence.  Every  electrolytic  reaction  will 
be  found  to  be  accompanied  by  some  changes  in  the 

1  "  Inadequacy  and  Inconsistency  of  Some  Common  Chemical 
Terms  "  —  Metallurgical  &  Chemical  Engineering,  December  1, 
1916,  p.  649. 


98  ELECTROCHEMICAL  EQUIVALENTS 

valences ;  this  seems  moreover  to  be  a  necessary 
consequence  from  the  above  conception  that  the 
electric  current  is  always  accompanied  by  the  making 
or  breaking  of  bonds  in  charging  or  discharging  the 
ions ;  it  moreover  seems  to  be  in  entire  agreement 
with  the  modern  electronic  theory,  explained  in  Part 
II.  It  is  the  amount  of  this  change  of  valence  and 
not  the  valence  itself  which  in  all  cases  is  the  basis 
of  the  quantitative  electro-chemical  calculations.  The 
valence  factor  which  enters  into  these  calculations  is 
always  the  difference  between  the  valence  before 
and  after  the  reaction.  Calculations  are  sometimes 
simplified  and  easier  to  understand  by  basing  them 
on  the  changes  of  valence,  as  shown  elsewhere  in 
the  examples  where  both  methods  are  illustrated. 

As  every  bond  of  a  gram-atom  of  any  element 
means  that  one  faraday  accompanies  the  making  or 
breaking  of  it,  one  faraday  will  be  required  per  gram- 
atom  for  every  unit  change  of  valence.  To  reduce  a 
valence  say  from  3  to  2  (as  in  the  reduction  of  ferric 
to  ferrous  sulfate)  means  going  one  third  toward 
freeing  the  element  of  all  of  its  bonds,  that  is,  toward 
setting  it  free.  The  less  the  change  of  valence  the 
less  electricity  it  will  require  to  free  a  gram  of  that 
element  or  to  dissolve  it. 

In  the  cases  in  which  elements  in  combination  are 
set  free,  then-  valence  has  been  changed  from  the 
one  they  had  in  combination  to  zero,  hence  in  such 
cages  and  only  in  such  cases  is  the  change  of  valence 
numerically  equal  to  the  valence  which  they  had  in 
combination.  Faraday's  law  as  usually  stated  in 
textbooks  therefore  applies  only  to  this  case,  which 
however  is  the  more  usual  one.  But  there  are  cases 
in  which  nothing  is  set  free  (see  Examples  7,  8,  9,  and 
10)  tho  there  is  always  a  change  of  valence,  hence  to 


VALENCE  99 

become  universal  this  law  should  refer  to  the  change 
of  valence  and  not  to  the  valence  alone. 

Sign  of  the  valence.  To  carry  out  this  convenient 
and  useful  conception  of  the  change  of  valence  it  is 
sometimes  necessary  or  desirable  to  designate 
whether  a  valence  is  +  or  '-,  that  is,  whether  the 
respective  ions  in  electrolysis  carry  positive  or  nega- 
tive charges ;  if  positive  they  will  travel  with  the 
current  and  tend  to  go  to  the  cathode ;  if  negative 
they  will  travel  against  the  current  and  tend  to  go  to 
the  anode.  And  when  set  free  they  give  up  their 
charges  to  the  electrode,  after  which  they  must 
necessarily  have  a  valence  of  zero. 

The  conception  of  negative  valences  will  not 
generally  be  found  described  hi  chemical  treatises, 
as  chemists  do  not  as  a  rule  take  any  notice  of  the 
sign  of  the  valence,  but  it  is  often  of  advantage 
to  do  so  in  electrochemistry;  the  conception  of 
negative  valences  necessarily  follows  mathematically 
and  physically  from  the  fact  that  the  charges  have 
different  signs.  The  sign  is  concerned  with  the 
direction  of  the  current  or  with  what  might  be  called 
the  direction  of  the  chemical  reaction,  that  is,  whether 
a  reduction  or  an  oxidation  (adduction)  which  are 
chemical  opposites.  When  the  signs  become  reversed 
in  a  reaction  they  are  also  important  factors  in 
determining  the  electrical  quantities  hi  a  reaction,  as 
shown  below,  but  with  this  exception  the  signs  do  not 
affect  the  quantities,  hence  the  values  given  in  Table 
I  are  applicable  as  well  to  +  as  to  —  valences. 

As  every  one  of  these  bonds  joins  two  atoms  in  a 
combination,  it  necessarily  is  positive  with  reference 
to  one  of  them  and  negative  with  reference  to  the 
other.  Thus  in  water,  H2O,  when  the  two  bonds 
are  considered  with  reference  to  the  hydrogen  they  are 


100  ELECTROCHEMICAL  EQUIVALENTS 

positive,  but  with  reference  to  the  oxygen  they  are 
negative. 

Most  of  the  elements  will  in  electrolysis  always  go 
to  one  particular  electrode  and  never  to  the  other; 
that  is,  they  always  carry  a  charge  of  the  same  sign ; 
hydrogen  for  instance  always  carries  positive  charges 
and  therefore  goes  to  the  cathode,  while  oxygen 
carrying  negative  charges  always  goes  to  the  anode. 
The  valence  of  hydrogen  is  therefore  always  +  and 
that  of  oxygen  always  -. 

Some  of  the  elements,  however,  like  antimony, 
carbon,  chlorine,  nitrogen,  etc.,  sometimes  carry 
positive  and  sometimes  negative  charges.  Their 
valences  are  therefore  sometimes  +  and  sometimes  - , 
depending  upon  the  nature  of  their  combination ;  it  is 
always  the  same  in  the  same  combination,  at  least  hi 
all  usual  cases.  These  elements  must  therefore  be 
considered  as  having  both  a  reducing  and  an  oxidizing 
or  adducing  action,  depending  on  the  sign  of  their 
valence. 

Electrolysis  separates  a  compound  or  combination 
of  elements  into  two  constituents  carrying  charges  of 
different  signs.  The  compound  in  its  free  state  must 
be  considered  to  have  no  free  charge,  that  is,  a  zero 
valence,  it  being  combined  with  nothing  else.  From 
this  it  follows  that  the  valences  of  the  constituent 
elements  of  a  compound  multiplied  by  the  number  of 
their  atoms,  must  always  add  up  to  zero.  Thus  in 
nitric  acid,  HNO3,  +1  +  5  —  6  =  0;  or  in  sulfuric 
acid,  H2SO4,  +  2  +  6-8  =  0.  This  is  often  useful  in 
finding  the  sign  of  the  valence  of  one  of  the  con- 
stituents when  those  of  the  others  are  known. 

A  radical  as  a  whole  may  be  said  to  have  a  valence  ; 
thus  SO  4  has  a  valence  of  —  2,  as  it  must  balance 
with  the  +  2  in  H2SO4. 


VALENCE  101 

As  illustrations  of  changes  of  signs  of  the  valence, 
sulfur  in  H2S  has  a  valence  of  -  ?  while  in  the 
oxide  SO3  it  has  a  valence  +  6  to  baUn£e\tb£X$(  —  2V=^ 

-  6  of  the  03.    Hence  when  the -sulfur  is  adduced 
or  oxidized  from  the  former  state,  into >  4Jie[  iafte^Jte-. 
change  of  valence  is  from  -  2  to  +6  which  is  equal 
to   +  8,  the  change  of  valence  being  the  algebraic 
difference.    If   this    reaction    could    be    carried    out 
electrolytically  it  would  require  8  faradays  per  gram 
atom  of  sulfur,  and  not  4  as   it  would  be  if  the 
signs  were  neglected.    In  this  change  it  must  pass 
thru  zero  valence,  which  means  its  free  state. 

Another  illustration  is  the  adduction  or  so-called 
oxidation  of  methane  CH4  into  carbon  tetrachloride 
CC14.  In  the  former  it  seems  that  the  valence  ought 
to  be  stated  to  be  -4  and  in  the  latter  +  4,  hence  the 
change  of  valence  is  +  8  and  not  zero  as  it  would  be 
if  the  signs  were  neglected;  the  +  sign  before  the 
8  means  that  it  was  an  adduction  or  oxidation.  Or 
in  reducing  nitric  acid,  HNO3,  into  ammonia,  NH3, 
the  change  of  valence  of  the  nitrogen  is  from  +  5  to 

-  3,  the  difference  being  -  8,  and  not  2  as  it  would 
be  if  the  signs  were  neglected ;    the   —   sign  here 
means  that  it  was  a  reduction. 

Chemical  reactions.  In  electrolysis  the  only  purely 
chemical  reactions  which  accompany  the  current 
are  reductions  and  oxidations  (adductions)  in  the 
sense  of  these  terms  given  below.  They  are  chemi- 
cally the  same  kind  of  a  reaction,  differing  only 
in  their  sign  or  direction ;  each  is  the  direct  opposite 
or  reverse  of  the  other ;  hence  whatever  is  true  of  the 
one,  the  reverse  is  true  of  the  other. 

Reduction.  Chemical  reductions,  when  interpreted 
according  to  modern  accepted  theories,  always  mean 
a  reduction  or  loss  of  the  valence,  whether  from  +  to 


102  ELECTROCHEMICAL  EQUIVALENTS 

or  toward  0,  or  from  0  to  -,  or  from  +  to  -.  The 
reduced  products  always  go  to  the  cathode.  Reducing 
.hydrogen  :frdiri  water  is  a  reduction  of  its  valence 
from  +1  to  6  for  each  of  the  two  atoms.  When  the 
fo^kis'*  af e  rediiced'from  their  combinations  to  their 
free  state  their  valences  are  always  reduced  from  + 
to  0.  When  an  element  has  a  +  valence  hi  a  com- 
bination it  means  that  it  is  hi  an  oxidized  state  and  is 
capable  of  being  reduced,  either  toward  or  to  the  free  state 
or  hi  some  cases  even  beyond,  to  a  negative  valence. 

Every  lowering  of  the  valence  should  therefore  be 
embraced  in  the  general  term  chemical  reduction, 
even  tho  this  is  not  now  customary  ;  it  would  be  more 
consistent  and  uniform  to  do  so.  When  a  metal 
combines  with  free  oxygen,  the  metal  is  correctly 
said  to  have  been  oxidized,  but  the  oxygen  must  be 
said  to  have  thereby  been  reduced,  as  its  valence  has 
then  been  reduced  from  0  to  -2.  This  is  quite 
consistent  when  it  is  considered  that  the  oxidizing 
property  of  the  oxygen  has  thereby  been  reduced, 
combined  oxygen  being  a  less  powerful  oxidizing 
reagent  than  free  oxygen. 

In  a  general  way  chemical  reduction  also  means  the 
loss  of  bonds  and  the  loss  of  a  companion  element 
and  is  therefore  an  appropriate  term  which  can  con- 
sistently be  extended  to  include  all  these  features. 
In  the  author's  opinion  it  also  means  a  loss  of  the 
electric  charge,  whether  positive  according  to  the 
older  conceptions  or  negative  according  to  the  newer 
ones,  provided  the  conceptions  are  consistently 
interpreted,  as  described  below.1  According  to  some 

1  For  a  more  detailed  discussion,  see  article  on  "  Oxidation 
and  Reduction  in  Physical-Chemistry.  Consistency  of  Terms 
and  Conceptions,"  in  the  issue  of  May  1,  1917,  Metal.  &  Chem. 
Eng.,  1917,  page  507  by  Carl  Hering. 


VALENCE  103 

writers,  however,  reduction  is  claimed  to  be  a  gain  of 
negative  charges ;  at  the  present  writing  there  seems 
to  be  no  definite  physical  proof,  it  is  a  deduction 
involving  some  disputed  definitions. 

It  is  conventionally  assumed  all  the  world  over  that 
electricity,  water,  and  gas  flow  from  their  positive, 
high,  or  compressed  state  to  their  negative,  low,  or 
rarified  state,  as  is  usually  indicated  by  an  arrow; 
conventionally,  therefore,  it  is  the  positive  charge  of 
electricity  which  flows  in  the  direction  of  the  arrow ; 
a  loss  of  a  charge  therefore  means  that  it  was  a 
positive  charge.  According  to  the  older  conceptions 
reduction  takes  place  at  the  cathode,  as  it  ostensibly 
does,  hence  corresponds  to  a  reduction  or  loss  of  the 
positive  charge  which  that  ion  carried ;  after  the  ion 
has  been  set  free  it  has  a  zero  or  neutral  charge ; 
its  positive  charge  may  be  conceived  to  flow  into  the 
cathode  and  pass  off  as  the  current. 

According  to  the  more  modern  electronic  theory, 
however,  it  is  the  negative  electricity  which  is  con- 
ceived to  flow  in  the  opposite  direction,  a  positive 
charge  being  then  the  result  of  a  loss  of  negative 
electrons ;  a  loss  of  a  charge  therefore  means  that  it 
was  a  negative  charge.  And  according  to  the  modern 
dissociation  theory,  before  any  current  is  applied  and 
before  they  reach  the  electrodes  the  ions  have  already 
been  dissociated  or  ionized,  whereby  they  have 
received  their  charges ;  dissociation  means  decom- 
position, hence  a  reduction  of  the  cation.  The  true 
chemical  reduction  of  the  cations  therefore  really 
took  place  during  this  process  of  dissociation,  and  as 
they  are  then  left  with  a  positive  charge  there  has 
been  a  reduction  or  loss  of  negative  electrons  during 
the  actual  chemical  reduction.  The  final  freeing  of 
an  element  is  not  an  essential  part  of  reduction; 


104  ELECTROCHEMICAL  EQUIVALENTS 

ferric  salts  are  correctly  said  to  be  reduced  to  ferrous, 
yet  nothing  is  set  free  thereby.  The  final  freeing  of 
the  dissociated  ions  is  a  different  and  subsequent 
process,  and  is  not  the  real  reduction. 

Hence,  whether  based  on  the  conventional  or  on 
the  more  advanced  conceptions,  a  chemical  reduction 
in  electrolysis  always  corresponds  to  a  loss  or  reduc- 
tion of  electric  charges  as  well  as  of  valence. 

In  the  author's  opinion  it  should  be  clearly  under- 
stood that  this  loss  of  negative  electrons  must  be 
regarded  as  taking  place  during  the  process  of  chemi- 
cal reduction  or  dissociation,  hence  when  it  is  said 
that  H  in  HC1  for  instance  has  a  free  positive  charge, 
it  refers  only  to  those  atoms  of  the  H  which  have 
been  reduced  on  being  ionized  by  dissociation ;  those 
which  are  still  combined  as  HC1  have  no  free  charges, 
as  the  HC1  as  a  combination  has  no  free  charges, 
those  of  its  H  and  Cl  (which  are  equal)  being  then 
combined  forming  the  bond,  and  their  mutual  attrac- 
tion may  be  said  to  constitute  the  force  which  binds 
the  elements  to  each  other;  equal  and  opposite 
charges  always  result  in  electrical  neutrality. 

As  neither  the  free  H  nor  the  undissociated  com- 
bination HC1  as  such,  has  any  free  charge,  there  can 
be  no  loss  or  gain  of  free  charges  during  the  oxidation 
of  H  to  HC1;  the  charges  which  the  H  and  Cl  gain 
and  lose  when  they  combine  are  equal  and  opposite, 
hence  neutralize  each  other.  It  is  therefore  wrong, 
in  the  author's  opinion,  to  say  that  because  the  H  in 
HC1  is  usually  (and  correctly)  marked  with  a  +  sign 
above  it,  indicating  that  it  has  a  positive  charge,  it 
got  this  charge  when  it  was  oxidized  by  combining 
with  the  Cl.  It  really  got  this  free  positive  charge 
when  it  was  thereafter  reduced  again  by  dissociation ; 
the  indication  of  these  charges  therefore  applies 


VALENCE  105 

correctly  only  to  the  dissociated  compounds  and  not 
to  those  elements  which  are  still  undissociated. 

Oxidation  or  adduction.  Chemical  oxidation,  when 
interpreted  according  to  modern  accepted  theories, 
always  means  an  increase  or  gain  of  the  valence, 
whether  from  -  to  or  toward  0,  or  0  to  +,  or  -  to  +. 
The  oxidized  products  always  go  to  the  anode.  Oxi- 
dation of  course  is  independent  of  whether  the 
element,  oxygen  itself  is  involved  or  not.  Altho  by 
general  consent  the  term  oxidation  has  been  extended 
to  include  combinations  with  other  elements  also, 
Cu  +  Cl  =  CuCl  being  called  an  oxidation,  yet  it  is 
thought  by  some  prominent  chemists  that  a  less 
confusing  and  a  more  consistent  and  appropriate 
term  would  be  desirable ;  among  all  those  suggested 
the  best  seems  to  be  "  adduction,"  1  as  the  prefix 
"ad-"  implies  addition  to  the  valence,  bonds,  ele- 
ments, and  charges,  as  explained  above  in  the 
reverse  sense  for  reduction,  the  prefix  "  re-  "  implying 
a  reduction  of  them;  each  is  then  the  exact  reverse 
of  the  other.  This  term  adduction  has  been  adopted 
in  this  book  as  preferable  to  oxidation. 

What  was  said  above  concerning  reduction  therefore 
applies  hi  the  reverse  sense  to  adduction  or  oxidation, 
hence,  in  the  sense  explained  above,  it  is  always 
accompanied  by  a  gain  of  valence  and  negative 
charges,  and  in  a  general  sense  by  a  gain  of  bonds 
and  companion  elements. 

When  an  element  in  combination  has  a  negative 
valence  it  means  that  it  is  in  a  reduced  state  and  is 

1  Suggested  independently  by  Dr.  Frederick  H.  Getman, 
one  of  the  present  authors,  but  was  subsequently  found  to  have 
been  proposed,  for  similar  reasons,  by  Dr.  M.  L.  Hamlin  in  a 
paper  by  Nelson  &  Falk,  Jour.  Am.  Chem.  Soc.,  35,  December, 
1913,  p.  1812. 


106  ELECTROCHEMICAL  EQUIVALENTS 

capable  of  being  adduced  or  oxidized  to  a  positive 
valence,  either  to  or  toward  the  free  state  or  even 
beyond. 

To  combine  a  free  element  with  oxygen,  fluorine, 
etc.,  which  is  called  oxidation  or  adduction  of  that 
element  (but  not  of  the  oxygen),  is  to  increase  its  va- 
lence from  0  to  +.  But  the  setting  free  of  sulfur  from 
H2S  for  instance  is  also  an  increase  of  its  valence 
from  -  2  to  0 ;  it  must  therefore  also  be  considered 
broadly  as  an  adduction  or  oxidation,  and  in  H2S  the 
sulfur  must  be  considered  to  be  in  even  a  more 
highly  reduced  state  than  when  free ;  it  can  be 
further  oxidized  to  SO3  and  its  valence  then  becomes 
+  6.  It  is  also  exactly  the  same  process  as  setting 
free  oxygen  from  an  oxide,  as  the  valence  of  the 
oxygen  has  thereby  been  increased  from  —  2  to  0 ; 
it  would  seem  to  be  preferable  to  call  this  '  *  adduced 
oxygen  "  rather  than  "  oxidized  oxygen ;  "  such  free 
oxygen  has  a  greater  oxidizing  power  than  when 
combined,  this  power  having  been  added  to  or  in- 
creased ;  the  inconsistency  lies  in  the  terms  and  not 
in  the  physical  facts. 

In  the  case  of  cuprous  chloride,  CuCl,  the  chlorine 
has  a  negative  valence  and  at  the  anode  it  tends  to 
be  adduced  or  oxidized  to  its  free  state.  In  that  case 
its  adducing  or  oxidizing  power  has  been  increased 
and  therefore  it  tends  to  adduce  or  oxidize  some  of 
the  remaining  CuCl  to  the  cupric  salt  CuCl2  (see 
Example  10). 

Numerical  values  of  the  valences.  The  valences  which 
the  elements  have  in  then*  different  compounds 
are  given  above  in  Table  IV  revised  for  this  book  by 
the  kindness  of  Dr.  Jos.  W.  Richards.  The  signs 
which  these  valences  have  are  included  hi  each  case. 
The  table  gives  what  he  calls  the  "  practical  va- 


VALENCE  107 

lences,"  that  is,  the  actual  ones  irrespective  of  any 
interpretation  involving  what  are  called  structural 
formulas. 

Some  of  the  elements,  like  hydrogen,  silver,  zinc, 
oxygen,  etc.,  practically  have  only  one  valence  in  all 
their  usual  combinations,  hence  they  each  have  but 
one  electrochemical  equivalent;  but  some  other 
elements,  like  copper,  iron,  nitrogen,  etc.,  may  some- 
times have  one  valence  and  sometimes  another,  hence 
they  have  several  electrochemical  equivalents.  With 
some  of  the  latter  the  electrochemical  reaction  merely 
changes  the  valence  from  one  of  its  values  to  another, 
in  which  case  they  may  have  still  another  equivalent 
corresponding  to  this  change ;  with  iron,  for  instance, 
there  can  be  a  change  of  valence  of  1,  yet  it  never 
has  this  valence.  With  most  of  the  elements  the  sign 
of  the  valence  is  either  always  +  or  always  -,  in  all 
their  compounds,  but  with  some  of  them,  namely 
antimony,  arsenic,  bromine,  carbon,  chlorine,  iodine, 
nitrogen,  phosphorus,  selenium,  silicon,  sulfur,  and 
tellurium,  the  valences  are  sometimes  +  and  some- 
times -,  tho  always  the  same  in  the  same  combina- 
tion, at  least  in  all  usual  cases. 

In  the  usual  electrolytes  (tho  rare  exceptions  are 
claimed  to  exist)  the  following  general  rules  may  be 
of  service :  The  valence  of  hydrogen  is  always  +  1 
(tho  perhaps  +  2  in  H2O2),  oxygen  always  -  2, 
chlorine  in  chlorides  -1,  SO4  in  sulfates  —  2,  NO3 
-  1,  C1O3  -  1 ;  in  metallic  solutions  in  which  the 
metal  is  the  base,  the  valence  of  the  metals  is  +  and 
that  of  the  radical  — . 

As  described  above,  when  the  valences  are  given 
their  proper  signs  and  when  multiplied  by  the  number 
of  the  atoms  of  an  element,  they  must  always  add  up 
to  zero  in  any  compound.  Thus  in  nitric  acid,  HNO3, 


108  ELECTROCHEMICAL  EQUIVALENTS 

+  1  +  5-6  =  0,  or  in  ferric  sulfate,  Fe2(SO4)3, 
2(+  3)  +  3(6-  8)  =  +  6  -  6  =  0.  As  every  one  of 
these  bonds  has  a  positive  and  a  negative  end,  the 
number  of  the  positive  ends  must  of  course  equal  the 
number  of  negative  ones.  This  principle  may  be 
used  to  determine  the  valence  and  its  sign,  for  one 
element  of  a  compound  when  those  for  the  others  are 
known. 

The  valence  of  an  element  can  also  often  be  de- 
termined by  finding  the  number  of  hydrogen  atoms 
which  will  replace  that  element  in  an  analogous 
compound.  Thus  silver  has  a  valence  of  1  because 
in  silver  nitrate,  AgNO3,  it  replaces  one  of  hydrogen  in 
the  analogous  compound  nitric  acid,  HNO3.  Or  the 
valence  of  silicon  is  4  because  in  its  oxide,  SiO2,  it 
replaces  four  atoms  of  hydrogen  in  the  oxide  of 
hydrogen  2(H2O),  when  the  amount  of  oxygen  is 
made  the  same  in  both;  the  valence  of  oxygen  is 
here  considered  to  be  the  same  in  both,  it  being 
assumed  to  have  only  one  valence,  an  assumption 
which  seems  to  be  generally  accepted,  tho  it  is  some- 
times contested. 

The  valences  of  the  radical  or  ion  SO4  must  be  -  2 
because  hi  H2SO4  the  hydrogen  has  a  valence  of  +  1, 
hence  +2-2  =  0.  Knowing  the  valences  of  SO4  to 
be  —  2,  that  of  iron  in  the  ferric  sulfate  Fe2(SO4)3 
must  be  +  3  because  2(+  3)  +  3(-  2)  =  0. 

These  simple  rules  will  suffice  for  most  cases 
occurring  in  the  ordinary  and  usual  electrochemical 
calculations ;  there  may  be  some  complicated  cases 
in  which  there  is  some  doubt ;  in  such  cases  one 
should  either  consult  a  chemist  or  make  the  electro- 
chemical calculation  by  some  indirect  method  by 
using  some  other  element  of  which  the  valence  is 
known,  like  hydrogen,  and  then  find  by  purely 


VALENCE  109 

chemical  calculation  what  the  chemically  equivalent 
amount  is  of  this  other  element  in  terms  of  the  one 
involved  in  the  problem.  Examples  illustrating  this 
method  are  given  in  Section  IV,  altho  there  is 
probably  no  doubt  in  any  of  these  as  to  what  the 
valences  are. 

Strength  or  intensity  of  bonds.  Each  of  these  chemical 
bonds  in  electrolytes  represents  the  same  quantity 
of  electricity,  namely  one  faraday,  which  is  the 
charge  carried  by  a  univalent  or  monovalent  gram- 
ion,  and  is  therefore  the  same  for  all  the  elements, 
yet  what  might  be  called  the  strengths  or  intensities 
of  the  bonds,  measured  in  terms  of  the  energy  which 
they  represent  when  made  or  broken,  is  quite  different 
in  different  combinations  of  elements. 

As  all  these  bonds  are  alike  in  the  quantity  of 
electricity  which  they  represent,  it  follows  that  the 
greater  the  number  of  these  bonds  in  any  combina- 
tion, that  is,  the  greater  the  valence,  the  greater  will 
be  the  quantity  of  electricity  involved.  In  this  sense 
the  greater  the  valence  the  greater  the  strength  or 
intensity  of  the  total  combining  power.  But  quantity 
of  electricity  by  itself  is  not  energy,  hence  it  does  not 
represent  the  strength  or  intensity  in  the  sense  of 
energy ;  it  is  only  one  factor  of  energy  in  the  same 
sense  that  either  feet  or  pounds  are  only  one  of  the 
factors  of  foot-pounds  of  energy.  Coulombs  or 
ampere-hours  must  be  multiplied  by  volts  hi  order 
to  express  the  energy.  The  so-called  heat  of  com- 
bination of  a  chemical  reaction  (more  correctly 
the  energy  of  combination,  as  in  electrolysis  this 
energy  does  not  appear  as  heat)  truly  expresses  the 
energy. 

While  these  unit  bonds  represented  by  a  faraday 
are  alike  for  all  elements,  yet  the  energy  represented 


110  ELECTROCHEMICAL  EQUIVALENTS 

by  a  unit  bond  may  be  and  generally  is  quite  different 
for  the  different  elements  and  even  for  the  same 
element  in  different  combinations.  The  true  strength 
or  intensity  or  degree  of  chemical  affinity  is  better 
expressed  in  terms  of  energy.  The  energy  in  joules 
(the  product  of  the  volts  and  the  coulombs)  repre- 
sented by  one  of  these  bonds  is  equal  to  the  faraday 
expressed  in  coulombs,  namely  96,500,  multiplied  by 
the  volts  required  for  producing  the  chemical  separa- 
tion (an  endothermic  reaction),  or  by  the  volts 
generated  by  their  formation  in  the  case  of  a  battery 
(an  exothermic  reaction).  For  instance,  in  the 
decomposition  of  a  gram-molecule  of  water,  H2O, 
there  are  two  bonds  each  representing  96,500  cou- 
lombs ;  if  the  decomposition  voltage  is  1.5  the 
strength  of  each  bond  measured  in  terms  of  energy 
is  96,500  x  1.5  =  144,750  joules ;  and  as  one  joule 
=  0.000,2778  watt-hours,  this  is  equal  to  40.2  watt- 
hours.  As  there  are  two  bonds^the  total  strength  is 
80.4  watt-hours;  this  means  that  it  will  take  80.4 
watt-hours  of  energy  to  decompose  a  gram  molecule 
of  water  equal  to  about  2  +  16  =  18  grams.  If  the 
value  of  the  faraday  is  taken  in  ampere-hours,  namely 
26.80,  and  is  then  multiplied  by  the  volts  (1.5),  giving 
40.20  watt-hours  per  bond,  the  calculation  becomes 
simpler.  But  great  care  must  be  taken  hi  using  the 
correct  voltage  of  decomposition,  as  other  factors 
enter  when  it  is  measured ;  the  voltage  here  referred 
to  is  that  determined  from  the  so-called  heat  of 
chemical  combination  usually  stated  in  calories. 
For  monovalent  ions  the  number  of  volts  is  equal  to 
this  energy  of  combination  expressed  in  kilogram 
calories  per  gram-molecule,  divided  by  23.061 ;  for 
multivalent  ions  this  constant  must  be  multiplied  by 
the  valence. 


VALENCE  111 

For  calculations  of  the  energies  involved  in  electro- 
chemical reactions  other  than  those  stated  in  the 
headings  of  the  columns  of  Table  I,  appropriate 
treatises  should  be  consulted,  as  this  is  beyond  the 
intention  of  the  present  descriptive  remarks  on 
valence. 

C.  H. 


Appendix  II 

ELEMENTARY  PRINCIPLES   OF  CHEMICAL 
REACTIONS  AND   CALCULATIONS 

The  following  brief  statements  of  a  few  of  the 
elementary  principles  of  chemistry  are  given  here  tc 
enable  one  who  is  not  a  chemist  to  follow  more 
intelligently  the  chemistry  necessarily  involved  hi  the 
electrochemical  calculations  described  in  this  book, 
For  the  less  usual  kinds  of  calculations  some  further 
knowledge  of  chemistry  may  be  necessary,  while  for 
the  more  involved  problems  treatises  on  chemistry 
must  be  consulted.  For  some  of  the  more  complex 
cases  the  necessary  facts  are  not  yet  known,  and 
then-  explanations  are  still  controversial. 

Elements;  atoms;  molecules;  radicals;  combinations;  sub- 
scripts. There  are  known  at  present  83  elementary 
substances,  called  the  chemical  elements,  which  alone 
or  hi  various  combinations  with  each  other  constitute 
all  matter;  they  are  all  given  in  Table  I,  and  are 
generally  represented  by  the  symbols  given  in  the 
second  column.  For  convenience  hi  describing  the 
reactions  between  these  elements  and  for  making 
calculations,  it  is  assumed  that  certain  extremely 
small  unit  particles  of  them  exist,  called  atoms. 
Chemical  compounds  are  made  up  of  various  com- 
binations of  these  atoms,  and  are  represented  by 
formulas  in  terms  of  then*  symbols ;  in  a  compound 
the  numbers  of  these  atoms  in  the  smallest  possible 
particle  of  the  compound,  which  is  called  a  molecule, 

112 


CHEMICAL  REACTIONS  AND  CALCULATIONS     113 

are  indicated  by  subscripts.  Thus  H2O  means  that  in 
this  compound  two  atoms  of  hydrogen  (H)  and  one  of 
oxygen  (O)  are  combined  to  form  one  molecule  of 
this  chemical  compound,  which  is  water.  CuSO4 
means  that  one  atom  of  copper  (Cu),  one  of  sulfur  (S), 
and  four  of  oxygen  (O)  are  combined  to  form  one 
molecule  of  what  is  called  copper  sulfate.  Subscripts 
therefore  denote  the  number  of  the  atoms  of  any 
particular  element  in  a  molecule.  These  compounds 
are  formed  by  the  union  of  these  atoms  in  those 
proportions,  and  they  may  be  decomposed  again  into 
then*  elements  by  breaking  this  union.  Sometimes  a 
fractional  part  of  a  molecule  is  for  convenience  called 
a  radical,  but  it  does  not  exist  by  itself;  thus  SO4 
is  a  radical  in  CuSO4,  ZnSO4,  Fe2(SO4)3.  In  elec- 
trolysis a  radical  may  sometimes  be  considered  to  act 
like  an  element;  thus  in  the  electrolysis  of  CuSO4 
the  Cu  goes  to  the  cathode  and  the  SO4  to  the  anode. 

Electrolytes;  electrodes.  If  hi  their  liquid  states, 
either  molten  or  dissolved,  these  compounds  conduct 
an  electric  current  and  are  decomposed  by  it,  they  are 
called  electrolytes.  The  passage  of  a  current  thru 
them  always  changes  them  chemically  in  some  way 
(reduction,  adduction,  or  oxidation)  at  the  two  places 
where  the  current  enters  and  leaves  the  liquid ; 
these  places  are  at  what  are  called  the  electrodes; 
the  one  thru  which  the  current  enters  the  liquid  is 
called  the  anode,  and  the  one  thru  which  it  leaves, 
the  cathode ;  this  is  true  whether  the  current  enters 
from  an  outside  source,  as  hi  the  case  of  an  elec- 
trolytic bath,  or  whether  it  is  generated  internally  as 
in  a  battery. 

Reactions;  equations;  coefficients.  When  brought  into 
contact  with  each  other,  many  of  these  chemical 
compounds  act  in  various  ways  on  each  other,  pro- 


114  ELECTROCHEMICAL  EQUIVALENTS 

ducing  chemical  changes ;  these  actions  are  called 
chemical  reactions ;  they  are  generally  expressed  in 
the  form  of  an  equation  showing  the  constitution 
of  the  mixture  before  and  after  the  reaction.  The 
number  of  atoms  has,  of  course,  not  been  changed, 
hence  must  always  be  the  same  on  both  sides  of 
these  equations.  The  number  of  molecules  of  these 
substances  required  to  produce  these  reactions  is 
indicated  by  numbers  preceding  them  called  coeffi- 
cients. Thus 

3  Pb  +  8  (HNO3)  =  3  Pb(NO3)2  +  2  NO  +  4  H2O 
means  that  three  atoms  of  lead,  Pb,  and  eight  mole- 
cules of  nitric  acid,  HNO3,  will  react  on  each  other  to 
produce  three  molecules  of  nitrate  of  lead,  Pb(NO3)2, 
and  in  doing  so  will  set  free  two  molecules  of  nitric 
oxide  gas,  NO,  and  four  molecules  of  water,  H2O  ;  the 
number  of  atoms  of  each  kind  before  and  after  the 
reaction  will  be  found  to  be  the  same,  and,  of  course, 
must  always  be  made  to  be  the  same  in  writing  out 
the  equation  to  make  it  balance.  The  coefficients  2, 
3,  4,  and  8  in  the  above  equations  indicate  the  number 
of  molecules  involved. 

When  with  the  aid  of  platinum  electrodes  an  elec- 
tric current  is  then  passed  thru  a  solution  of  this 
nitrate  of  lead,  which  is  an  electrolyte,  it  decomposes 
this  salt  into  one  atom  of  free  lead,  Pb,  one  of 
oxidized  lead,  PbO2,  and  one  of  nitric  acid,  HNO3. 
The  reactions  before  and  after  are  then  shown  by  the 
following  equation,  which  in  order  that  it  shall  balance 
must  include  two  molecules  of  water,  H2O,  which 
also  enters  into  the  reaction. 

2  Pb(NO3)2  +  2  H2O  =  Pb  +  4  HNO3  +  PbO2 

Relative  weights;  atomic,  molecular,  and  formula  weights. 
The  relative  weights  of  the  atoms  of  the  elements, 


CHEMICAL  REACTIONS  AND  CALCULATIONS     115 

that  of  oxygen  being  by  convention  assumed  to 
be  16,  are  called  the  "  atomic  weights "  and  are 
given  in  column  3  of  Table  I.  Adding  together  the 
atomic  weights  of  all  the  atoms  forming  a  molecule, 
being  careful  to  note  the  subscripts  (the  coefficients 
are  not  concerned),  gives  the  so-called  molecular 
weight,  or  preferably  the  formula  weight,  of  the  whole 
molecule,  and  the  proportional  part  of  this  total 
weight  which  is  due  to  any  one  of  the  elements,  or 
group  of  elements,  is  then  easily  determined  by 
simple  proportion.  Thus  for  nitrate  of  lead,  Pb(NO3)2, 
taking  the  respective  atomic  weights  from  the  table 
gives  the  molecular  or  formula  weight :  207.20  + 
2  (14.01  +  16  x  3)  =  331.22.  The  lead  forms  207.20 
~  331.22  =  .626  of  it  (62.6%)  or  nearly  2/3 ;  the  two 
parts  of  the  radical  NO3  form  the  other  third  ;  and  the 
six  oxygen  atoms  (6  x  16  =  96)  form  96  +  331.22  = 
.29  or  nearly  30  %  of  it. 

Actual  weights;  gram-atoms;  gram-molecules;  gram-ions. 
Such  atomic  weight  calculations  however  give  merely 
relative  weights  or  proportions,  but  not  absolute 
weights  in  grams  or  pounds.  In  order  to  get  the 
latter  all  these  ideal  diminutive  atoms  are  for  con- 
venience supposed  to  be  enlarged  the  same  number 
of  millions  of  times  until  the  enlarged  oxygen  atom 
weighs  16  grams,  then  all  the  actual  weights  of  the 
correspondingly  enlarged  atoms  of  all  the  other 
elements  will  be  as  many  grams  as  is  expressed 
numerically  by  their  atomic  weights.  These  are 
called  gram-atoms  or  sometimes  "  one  atomic 
weight ; "  or  when  added  together  for  a  molecule 
they  are  called  gram-molecules.  They  then  become 
tangible  quantities  which  are  easily  weighed,  a  gram- 
molecule  of  water  for  instance  being  about  18  grams, 
or  18  cubic  centimeters ;  a  gram-atom  of  copper  being 


116  ELECTROCHEMICAL  EQUIVALENTS 

63.57  grams  or  about  a  seventh  of  a  pound.  Simi- 
larly in  electrochemistry  a  gram-ion  means  an  ion  or 
electrochemical  unit  which  weighs  as  many  grams  as 
is  expressed  by  the  sum  of  the  weights  of  its  con- 
stituent parts. 

Valence.  When  an  atom  combines  with  or  can 
replace  only  one  atom  of  hydrogen,  it  is  said  to  have 
a  valence  of  1 ;  when  it  combines  with  or  replaces 
2,  3,  4,  etc.,  atoms  of  hydrogen,  its  valence  is  2,  3,  4, 
etc.,  respectively.  Some  elements  have  several  va- 
lences. The  subject  of  valence  hi  electrochemistry  is 
treated  more  fully  hi  Appendix  I. 

Chemical  equivalents.  By  a  chemical  equivalent  or 
equivalent  weight  or  combining  proportion,  is  meant 
that  chemical  quantity  or  amount  of  a  substance  which 
can  chemically  replace  or  be  substituted  for  or  com- 
bine with  another,  or  which  in  a  chemical  equation 
corresponds  to  another.  Thus  hi  sulfuric  acid,  H2SO4, 
two  hydrogen  atoms  are  the  chemical  equivalent  of 
one  of  copper  in  CuSO4,  as  each  could  quanti- 
tatively replace  the  other;  a  given  electric  current 
will  electrolyze  chemically  equivalent  amounts  of 
different  substances,  hence  a  current  which  will  set 
free  2  gram  atoms  of  H  (2.016  grams),  will  set  free 
one  gram  atom  (63.57  grams)  of  Cu  from  CuSO4. 
Furthermore  H2  and  SO4  may  be  said  to  be  chemically 
equivalent  amounts  as  they  combine  in  those 
amounts ;  so  are  Cu  and  SO4.  Or  in  the  equation 

Al  +  3  HC1  =  AlCls  +  3  H 

one  of  aluminum,  Al,  and  three  of  hydrochloric  acid, 
HC1,  may  be  said  to  be  chemically  equivalent,  or 
chemically  combining  quantities,  for  in  any  other 
proportions  they  would  not  form  this  product.  Hence 
for  every  pound  of  aluminum  to  be  dissolved  the 


CHEMICAL  REACTIONS  AND  CALCULATIONS     117 

chemically  equivalent  amount  of  hydrochloric  acid 
required  (not  including  the  water  in  which  the  acid  is 
dissolved)  is  easily  calculated,  it  being  in  the  propor- 
tion of  the  atomic  weights  or  formula  weights  in  the 
equation,  namely  as  3  (1.008  +  35.46)  =  109.4  is  to 
27.1 ;  that  is,  1  pound  of  aluminum  will  require 
109.4/27.1  =  4.04  pounds  of  acid. 

Reduction  and  adduction  or  oxidation.  As  far  as  the 
chemical  changes  produced  by  electrolysis  are  con- 
cerned there  are  in  general  two  classes  of  chemical 
reactions  called  reduction  and  adduction  or  oxidation ; 
they  are  the  direct  opposites  of  each  other,  each  being 
the  reversal  of  the  other ;  they  are  the  same  in  kind 
but  opposite  in  direction  or  sign.  When,  for  instance, 
a  metal  has  been  obtained  in  its  free  state  from  a 
solution  of  it,  say  in  an  acid,  the  metal  is  said  to  have 
been  reduced;  while  when  a  free  metal  has  been 
dissolved  say  by  an  acid  and  brought  into  a  state  of 
solution,  the  metal  is  said  to  have  been  oxidized,  but 
as  this  term  is  confusing  and  misleading  when  this 
combining  element  is  some  other  one  than  oxygen 
the  new  term  adduction  (the  antithesis  of  reduction) 
is  here  recommended.  (See  further  reference  to  it 
under  Valence,  Appendix  I.)  For  instance,  metallic 
copper  obtained  from  the  solution  CuCl2  is  said  to 
have  been  reduced;  while  when  metallic  copper  is 
dissolved  by  hydrochloric  acid  to  form  CuCl2  it  is 
said  to  have  been  adduced  or  oxidized.  Electro- 
chemically  there  is  always  apparently  a  chemical 
reduction  of  some  kind  at  the  cathode  (like  the 
deposition  of  a  metal),  and  a  chemical  adduction  or 
oxidation  at  the  anode  (like  the  dissolving  of  a  metal). 

Chemical  affinity.  Some  elements  or  groups  of 
elements  have  a  very  strong  tendency  to  combine 
while  with  others  it  is  weak,  and  with  still  others 


118  ELECTROCHEMICAL  EQUIVALENTS 

there  is  none  at  all ;  the  stronger  affinity  will  in 
general  overpower  the  weaker.  In  electrochemical 
calculations  involving  merely  the  quantities  of  sub- 
stances set  free  or  dissolved  or  changed  by  a  given 
current,  that  is,  in  such  as  are  calculated  with  the 
aid  of  the  present  tables,  this  factor  of  affinity  does 
not  enter,  as  a  given  current  will  set  free  or  dissolve 
the  same  amount  of  any  one  element  whether  that 
element  is  tightly  or  loosely  combined  with  other 
elements,  provided  that  the  valence  is  the  same. 
The  intensity  of  this  chemical  affinity  will  have  an 
effect  on  the  voltage  that  is  required  to  bring  about 
the  reactions  or  is  produced  by  it,  but  it  has  no  effect 
on  the  number  of  coulombs  or  ampere-hours  that  are 
required  for  electrolyzing  a  given  quantity  of  the 
material. 

Primary  and  secondary  reactions.  In  electrolysis  the 
current  will  produce  certain  chemical  reactions,  after 
which  the  products  produced  may  react  chemically  on 
each  other  or  on  some  other  substance  present ;  the 
former  is  called  a  primary  reaction  and  the  latter  a 
secondary  one,  as  it  is  not  produced  directly  by  the 
current.  In  the  electrolysis  of  sulfuric  acid,  H2SO4, 
for  instance,  the  hydrogen  is  set  free  at  the  cathode 
which  is  a  true  primary  reaction ;  but  the  SO4  which 
goes  to  the  anode,  cannot  exist  as  such  and  therefore 
combines  with  the  hydrogen  of  the  water  always 
present,  setting  free  oxygen  at  the  anode.  This  latter 
is  sometimes  called  a  secondary  reaction,  tho  on  the 
other  hand  it  may  be  claimed  that  the  electrolytic 
process  has  not  been  completed  until  definite  com- 
pounds have  been  produced,  and  not  merely  radicals. 
It  may  also  be  said  that  as  the  amount  of  sulfuric 
acid  is  the  same  after  the  reaction  as  before,  while 
the  water  diminishes,  it  was  the  water  and  not  the 


CHEMICAL  REACTIONS  AND  CALCULATIONS     119 

acid  which  was  electrolyzed.  If  the  anode  is  of 
copper  it  will  be  dissolved  by  the  SO4  ions  forming 
CuSO4,  which  would  seem  to  be  a  true  primary 
reaction. 

It  is  sometimes  difficult  to  discriminate  between  the 
two  reactions ;  in  some  cases  authorities  differ  and  no 
generally  accepted  definitions  to  distinguish  clearly 
between  them  seem  to  exist ;  but  when  reactions  do 
not  take  place  exactly  simultaneously  with  the  passage 
of  the  current  and  in  exact  proportion  to  it,  or  when 
they  continue  after  the  current  ceases,  they  are 
unquestionably  secondary.  The  author  suggests  that 
in  view  of  the  fact  that  some  energy  changes  are 
generally  involved  in  all  chemical  and  electrochemical 
reactions,  a  primary  reaction  may  be  said  to  be  the 
one  whose  energy  (endothermic  or  exothermic) 
appears  in  the  electric  circuit,  while  a  secondary 
reaction  is  one  whose  energy  does  not  appear  in  the 
electric  circuit. 

C.  H. 


Appendix  III 


CONVERSION  FACTORS  USED   IN  ELECTRO- 
CHEMICAL  CALCULATIONS 

Taken  from  Bering's  "  Conversion  Tables." 
Length. 

1  centimeter  =     0.3937  inch 

1  inch  =      2.540  centimeters 


Surface. 
1  sq.  inch 
1  sq.  decimeter 
1  sq.  decimeter 
1  sq.  foot 

Volumes. 
1  cb.  centimeter 
1  cb.  centimeter 
1  cb.  inch 
1  quart 
1  liter 
1  liter 
1  gallon 
1  gallon 
1  cb.  foot 
1  cb.  foot 

Weights  or  Masses. 
1  gram 

1  pennyweight  (troy) 
1  ounce  (advp.) 
1  ounce  (troy) 
1  pound  (advp.) 
1  kilogram 

Weights  and  Volumes. 
1  pound  per  gallon 
1  kilogram  per  liter 


6.452  sq.  centimeters 
15.50  sq.  inches 
0.1076  sq.  foot 
9.290  sq.  decimeters 


1  milliliter 

0.06102  cb.  inch 
16.39  cb.  centimeters 

1.101  liters 

1.057  quarts  (U.  S. ;  liquid) 

0.2642  gallon  (U.  S. ;  liquid) 

3.785  liters 

0.1337  cb.  foot 
28.32  liters 

7.481  gallons  (U.S.;  liquid) 


15.432  grains 
1.555  grams 

28.35  grams 

31.10  grams 
0.4536  kilogram 
2.205  pounds  (avdp.) 


0.1198  kilogram  per  liter 
8.345  pounds  per  gallon 
120 


CONVERSION  FACTORS 


121 


Waler. 

1  liter 
1  gallon 
1  cubic  foot 
1  pound 
1  pound 
1  pound 
1  kilogram 

Energy  (heat). 


2.205  pounds 
8.345  pounds 
62.43  pounds 
0.4536  liter 
0.1198  gallon 
0.01602  cb.  foot 
0.2642  gallon 


1  joule  =      0.2389  gram  calorie 

1  thermal  unit  (BTU)  =  252.0  gram  calories 
1  watt-hour  =      0.8600  kg.  calorie 

1  kg.  calorie  =      3.968    thermal  units 

1  kg.  calorie  =      1.163    watt-hours. 


Power. 

Iwatt 

1  gram  calorie  per 

second 

1  horse-power 
1  kilowatt 


0.2389  gram  calorie  per  second 

4.186  watts 
0.7457  kilowatt 
1.341  horse-powers 


Electrochemical    Equivalents 
given  in  Table  I). 

Grams  per  watt-hour 

Kilograms  per  horse- 
power-hour 

Pounds  per  kilowatt- 
hour 

Pounds  per  horse- 
power-hour 


in    Energy   (other   than    those 


0.0373  x 
0.0278  x 
0.0822  x 


0.0613  x 


atomic  weight 


change  of  valence  x  volts 


Watt-hours  per  gram  =  26.8  x 
Kilowatt-hours  per 

pound  =  12.2  x 

Horse-power-hours  = 

per  kilogram  =  36.0  x 
Horse-power-hours 

per  pound  =    16.3  x 


change  of  valence  x  volts 
atomic  weight 


122 


ELECTROCHEMICAL  EQUIVALENTS 


Electrochemical  energy. 
For  monovalent  ions : 

Volts  =  kilogram  calories  per  gram  molecule   x  0.0434 
For  multivalent  ions  divide  the  volts  thus  obtained  by  the 

valence 


Electrolytic  deposits. 
1  gram  per  sq.  deci- 
meter 

1  pound  per  sq.  foot    = 
1  pound  per  year 

1  pound  per  year 

1  pound  per  day  (of  24 

hours) 

1  gram  per  minute 
1  short  ton  per  year 
1  pound  per  hour 


0.02048     pound  per  sq.  foot 
48.82  grams  per  sq.  decimeter 

0.002738    pound   per   day   (of    24 

hours) 
0.0008624  gram  per  minute 

0.1826         short  ton  per  year 
1160.  pounds  per  year 

5.476  pounds  per  day 

4.383  short  tons  per  year  (day 

of  24  hours) 


(The  year  is  considered  to  be  3654  days.) 


C.  H. 


Appendk  IV 


GLOSSARY 

The  numbers  refer  to  the  pages  on  which  the  definitions  or  explanations 
will  be  found. 


Adduction 105,  117 

"       at  anode. 5,  57,  117 

Affinity,  chemical 117 

Anions 55 

Anode 54,113 

Atom 112 

"  vs.  ion.  . 58 

Atomic  weight 114 

Atomicity 29 

Avogadro's  law 2 

Binary  electrolytes 69 

Bivalent 2 

Bond 9*2 

positive  and  negative  99 

"     unit 93 

Cathode 64,113 

"      particle 74 

"      rays 73 

Cations 65 

Change  of  valence 97 

Charge,  unit 64,  93 

Chemical  affinity 117 

Chemical  equivalents . .  63,  116 

Coefficient 113 

Combinations,  chemical . .   112 
Conductance,  electronic . .     85 

Copper  coulometer 68 

Corpuscle 78 

Coulomb 31,  65 

Coulometer. .  66 


Diatomic 2 

Direction  of  current 86 

Di-valent , 2,95 

Electrochemical  constant  64, 65 
"  equivalent     65 

Electrodes 54,  113 

Electrolysis 54,  113 

Electrolyte 53,64,55 

Electron 78 

Electrons,  valence 79 

Element 112 

Endothermic 110 

Equations,  chemical 113 

Equivalent,  chemical 116 

Exothermic 110 

Faraday,  the 3,  29,  93 

Faraday's  law 3,  5,  62,  64 

Formula  weight 114 

Fourth  state  of  matter 74 

Fundamental  law  for  gases 

1,  9,  23,  29 

Gram-atom 115 

Gram-ion 31,  115 

Gram-molecule 115 

Ion 55 

"  vs.  atom..  58 


Joule, 


110 


123 


124 


GLOSSARY 


Migrations  of  ions 55,  60 

Molecular  weight 114 

Molecule 112 

Mon-atomic 2 

Mono-valent 95 

Negative  valence 99 

Non-electrolytes 64 

Non-valent 95,  97 

Oxidation 105,  117 

"        at  anode ..  6,  57,  117 

Poles , 54 

Primary  reactions 118 

Quaternary  electrolyte ...     69 

Radiant  state  of  matter ...     74 

Radical 112 

Reactions 113 

"       primary 118 

"        secondary.  ..56,  118 

Reduction 101,  117 

"       at  cathode  5,  57,  117 
Relative  weights 114 

Salts 24 

Secondary  reactions ...  56,  118 


Sign  of  valence 99 

Silver  coulometer 66 

Subscripts 112 

Ternary  electrolyte 59 

Titration  coulometer 71 

Tri-valent 95 

Unit  bond 93 

"  charge 64 

Valence 5,  85,93,94,  116 

"      change  of 4,97 

"      electrons 79 

"      negative 99 

"      number  of  electrons  85 

"      sign  of 99 

"      unit  charges 64 

"      vs.  valency.  .....     97 

"      zero 5,96,97 

Valency 97 

Valent,  non- 95,  97 

Voltameter 66 

Volume  coulometer 69 

Water  coulometer 69 

Zero-valence 6,  95,  97 


INDEX 


Adduction,  defined.  .  .  106, 117 

"         again 105 

"  at  anode.  5,  67,  117 
"  examples....  42,  46 
"  sign  of  valence  99 

Affinity,  defined 117 

"      110 

Ampere-hours  per  cubic  foot  23 
"  "  per  gram..  12 
"  "  per  liter...  23 
"  "  per  pound.  12 

Anions,  defined 65 

Anode,  defined 64,  113 

"     consumption  of .  . .     33 

"     reaction 57 

Atom,  defined 112 

"      of  electricity....  84,  79 

"      stability  of 82 

"     structure  of 79 

"     vs.  ion 68 

Atomic  weight,  defined. . .   114 

"     table 12 

Atomicity 29 

Atoms,  number  of 86 

"     constitution  of 80 

Avogadro's  constant 9 

"          law,  defined. .       2 

B 

Battery,  depolarizer ....  36,  37 

"     poles  of 66 

"     storage 45 

Binary  electrolyte 59 

Bivalent 2 

Bond,  defined 92 


Bond 86 

"    non-electrolytic 95 

"    positive  and  negative  99 

"    strength  of 109 

"    unit 93 

Bunsen  cell 39 

Bureau  of  Standards  cou- 

lometer . .  67 


Calculations,  method  of . .     28 

Calories 110,121 

Cathode,  defined 54,  113 

"       particle 74 

"       rays,  defined ...     73 
"  "    deflection.     76 

"       reaction 57 

Cations,  defined 55 

Change  of  sign  of  valence 

48,  50,  101 
Change  of  valence,  defined 

4,97 
examples 
36,  37,  43,  48 
"        Table  I      8 

Charge,  free 104 

"       magnitude 77 

"      on  electron 86 

"      ratio  to  mass. ...     75 

"      value  of 78,79 

"      unit 64,93 

Charged  ions 58 

Chemical  affinity,  defined    117 

"  "       110 

"       calculations. ...   112 
"       compounds 24 


125 


126 


INDEX 


Chemical  equivalents,  defined 
63,  116 

"  "  32,91 

"      reactions,  defined  101 

"  "        112 

Chemistry,  elementary  prin- 
ciples     112 

Coefficients,  defined 113 

"         ignored 39 

Combination  heat 109 

Combinations,  defined  . . .    112 
"  of  elements, 

table  IV 24 

Combining  capacity 84 

Compounds,  chemical ....  24 
Conductance,  electronic . .  86 
Conduction,  electrolytic.  .  93 

Conductors,  class  of 63 

"          second  class .     85 

Conversion  factors 120 

Copper  anode 33 

"      chloride 38 

"      coulometer 68 

Corpuscles 78 

Coulomb,  defined 31,  65 

Coulombmeter,  see  coulome- 
ter       66 

Coulombs  per  cubic  c.m.      23 
"        per  milligram ..     12 

Coulometer,  defined 66 

"         Bureau  of  Stand- 
ards       67 

copper 68 

"  silver 66 

"  titration 71 

"  volume 69 

"  water 69 

"  weight 66 

Cubic  c.m.  per  coulomb . .     23 
"     feet  per  1000  amp.  hrs.23 

Current,  direction  of 85 

"       electronic  stream    85 


Decomposition  voltage ...   110 

Depolarizers 33,  36,  37 

Description  of  tables 7 

Diaphragm 66 

Diatomic 2 

Direction  of  current 85 

Discharge  in  vacuum 73 

Dissociation  theory 57 

"  "    applied  103 

Di-valent 2,  95 

"        element 83 

Double  duty,  of  acid 51 

"          "    of  current.  .  .   46 
Drop,  volume  of  a 78 


Electricity  is  not  energy .  .   109 

"        atom  of 79,84 

Electrochemical     constant, 

defined 64,  65 

Electrochemical  equivalent, 

calculations 28 

Electrochemical  equivalent, 

defined 65 

Electrochemical  equivalent 

by  weight 12 

Electrochemical  equivalent 

of  gases 23 

Electrochemical  reaction .      86 

Electrodes,  defined. .  .  .54,  113 

"          no  deposits  on     42 

Electrolysis,  defined ...  54,  113 

"  section  V 53 

Electrolyte 63,54,  65 

Electrolytic  conduction  . .     93 

Electron,  defined 78 

"       enlarged 93 

Electrons  connect  atoms  .  84 
"  distribution  of . .  80 
"  gain  and  loss  of 

85,  103,  105 


INDEX 


127 


Electrons,  mass  of 79 

source  of 79 

valence 79 

Electronic  conception  of 

conductance .     86 
conception  of 

valence 84 

current  stream      85 

"         theory 73 

theory,    deduc- 
tions      103 

Electrophysical  law 9,  23 

Elements,  defined 112 

"       combinations  of..     24 

"      list  of  the 12 

"      with  +  and  — - 

valences 107 

"      relation  to  elec- 
trons       80 

"      symbols  of 12 

"      valences  of 12,24 

Endothermic 110 

Energy  constant 110 

"  coulombs  x  volts..  109 
"  electrochemical  .  .  122 
"  of  combination ...  109 

"      of  reactions 109 

Equations,  chemical,  defined 

113 

Equivalent,    chemical,  de- 
fined. .    63,  116 
chemical,     32,  91 

Examples 28 

Exothermic .  .  .110 


Faraday,  the,  defined. 3,  29,  93 

"       3,7,29,98 

"       applied  to  calcu- 
lations   29,  31 

Faraday's  law,  defined 

3,  5,  62,  64 


Faraday's  law 93 

"          "    constants  of     4 
"          "    correction  of 

4,5 
limitations 

of    4,43,98 
"          "     universal  4,  99 

Force  of  migration 62 

Formula  weights,  defined .  114 
Fourth  state  of  matter. ...     74 

Free  charges 104 

Fundamental  constants,  by 

weight. . .       7 
constants,  gases 
1,  9,  23,  29 

data 7 

"  law,  by  weight    3 

"  "    gases 

1,  9,  23,  29 
laws..  1 


Gases,  equivalents  of ....     23 

Glossary  of  terms 123 

Gram-atom,  defined 115 

Gram-ion,  defined 31,  115 

Gram-molecule,  defined . .   115 

Grams  per  ampere-hour  12,  21 

"     per  watt-hour 12 


Heat  of  combination 109 

Horse-power 121 

Hydrogen,  example 33 

intermediate 

element ....  32 

"           weight  of 33 


Intensity  of  bonds 109 

Intermediate  reactions ....  40 
Involved  reactions . .  41 


128 


INDEX 


Ion,  defined 65 

"    vs.  atom 58 

Ions,  activity  of 59 


Joules 


110 


Kilograms  per  1000  amp.  hrs. 

12,21 
per  kilowatt-hour  12 

Kilowatt 121 

Kilowatt-hours  per  kilogram  12 


Liter  of  hydrogen,  weight.  33 
Liter  of  oxygen,  weight ...  9 
Liters  per  ampere-hour ...  23 


M 

Manganese  peroxide 
Mass,  ratio  to  charge 
Matter,  fourth  state  of . . 
Metallic  conductance .  .  . 

Methane,  oxidized 

Migration 

"        speeds  of .  .  .  . 
Milligrams  per  coulomb . 

Molecular  layer 

"      weight,  defined . 

Molecules,  defined 

Mon-atomic 

Mono-valent. . 


.  37 

.  75 

..  74 

.  85 

.  101 
55,  60 

.  61 

.  12 

.  55 

.  114 

.  112 

.  2 

.  95 

.  122 


ions 

N 

Negative  charge  flows 103 

"  "      sign 58 

.  "        valence 37,  99 

"  "      example 

48,50 
Nitric  acid  reduced .  .       .   101 


Non-conductor 63 

Non-electrolytes 54 

Non-valent 95,  97 

Nucleus,  positive 79 


Organic  compounds  non- 
conductors       54 

Oxidation,  defined 105,  117 

"         a  gain 105 

"  at  anode  5,  57,  117 
"  examples..  ..42,  46 
"  sign  of  valence.  99 

Oxygen,  weight  of  liter ....     9 


Poles,  defined 54 

Positive  charge  flows ....   103 
"  "      mass  of..     80 

"  "      sign  of...     58 

"  "      size  of...     80 

"      nucleus 79 

Pounds  per  1000  amp.  hrs.     12 
"      per  kilo  watt-hour.     12 

Practical  valences 106 

Primary  battery 34 

"        reactions,  defined  118 


Quaternary  electrolytes.  .     59 


Radiant  state  of  matter. . .     74 

Radical,  defined 112 

electrochemical 
constant  of  ...     43 

Reactions,  defined 113 

"         chemical 101 

"         intermediate . .     40 

"         involved 41 

"         primary  and  sec- 
ondary, def'd  118 


INDEX 


129 


Reactions,  secondary,  de- 
fined       56 

secondary  example  41 
Reduction,  defined.  . .  101,  117 

«  99 

"          again 103 

"         a  loss...     101,104 
"          at  cathode 

5,  57,  102,  117 
Reduction,  conception  of .    103 

"          example 42 

Relative  weights,  denned .   114 

S 

Salts 24 

Second  class  conductors .  .     85 
Secondary  reactions,  defined 

56,  118 

"  "    example  41 

Sign  of  valence 6,  99 

"     "      "       example.  48,  50 

Silver  coulometer 66 

"      standard  equivalent     7 

Speeds  of  ions 61 

Stability  of  atoms 82 

Storage  battery 45 

Strength  of  bonds 109 

Structural  formulas 24,  96 

Structure  of  atom 79 

Subscripts,  defined 112 

"        ignored 38 

Supersaturation 77 

Symbols  of  elements 12 


Ternary  electrolytes 59 

Thermal  unit 121 

Thermo-chemical,  equivalents 
109 

Titration  coulometer 71 

Tri-valent 95 

"          element  .  83 


Unit  bond 93 

"     charge 64 

Univalent  element. .  83 


Vacuum  discharge 73 

Valence,  defined 

5,  85,  93,  94,  116 

"       , 91 

"      a  number 97 

"      change  of,  defined 

4,97 

it  ft  - 

examples 
36,  37,  43,  48 
"       Table  I     8 
change  of  sign 

48,  50, 101 

"      electronic 84 

"      electrons 79 

"      fractional 95 

"      negative 37,  99 

"  "      example 

48,50 
number  of  electrons 

85 
of  compound =O 

50,  100,  107 
"      of  radical.  .  .  .43,  108 

"      rules 107 

"      sign  of 6,  99 

"      unit  charges.  ...     64 

"      vs.  valency 97 

"      zero 5,95,97,98 

"          "     example. 49,  98 
Valences  add  up  to  zero 

50,  100,  107 
numerical  values  of 
24,106 

practical 24,106 

of  the  elements, 
Table  IV..  24 


130 


INDEX   OF    AUTHORS 


Valency,  defined 97 

"        91 

"       a  property 97 

"       vs.  valence. ....     97 

Valent,  non- 95,  97 

Velocity  of  cathode  particles  74 
Voltage  of  decomposition .   110 

Voltameter,  defined 66 

Volume  coulometer. .  69 


W 

Water  coulometer 69 

Watt-hours 110 

"        per  gram 12 

"        per  pound 12 


Zero  valence 5,  95,  97,  98 

"         "     example.  .  .49,  98 
Zinc  in  battery 34 


INDEX  OF  AUTHORS 


Arrhenius 58 

Bates 71 

Blanchard 59 

Boernstein 9 

Bureau  of  Standards  VI,  7,  67 

Clarke 7 

Comstock 87 

Cox 87 

Crookes 73 

Daneel 71 

Falk 105 

Faraday 64,  62 

Friend 87 

Getman 105 

Hamlin 105 

Heimrod 66 

Hering  ...  .V,  93,  97,  102,  120 

Jones 59 

Kohlrausch . .  . .  *  70 


Landolt 9 

Le  Blanc 66 

Mellor 94 

Mendeleef 83 

Millikan 78 

Nelson 105 

Nicholson 80 

Oettel 68 

Perrin 74,  86 

Ramsay 84,  87 

Richards,  J.  W... VI,   24,    106 
Richards,  T.W 66 

Smith 94 

Stokes 78 

Talbot 59 

Thomson,  J.  J 74,  79,  87 

Troland 87 

Washburn 71 

Wilson. .  77 


YA 


995706 


Engineering 
Ltbnry 

THE  UNIVERSITY  OF  CALIFORNIA  UBRARY 


